
    617 A.2d 247
    STATE OF NEW JERSEY, PLAINTIFF-APPELLANT, v. JOSEPH M. SPANN, DEFENDANT-RESPONDENT.
    Argued November 27, 1990
    Decided January 5, 1993.
    
      
      Carol M. Henderson, Deputy Attorney General, argued the cause for appellant (Robert J. Del Tufo, Attorney General of New Jersey, attorney; Steven E. Lessick, Deputy Attorney General, of counsel and on the brief).
    
      
      Michael B. Einscklag, Designated Counsel, argued the cause for respondent (Wilfredo Caraballo, Public Defender, attorney).
   PER CURIAM.

Defendant, Joseph M. Spann, was convicted of sexual assault, a second-degree crime under N.J.S.A. 2C:14-2c(3). The statute criminalizes sexual penetration when the defendant has supervisory or disciplinary power, by virtue of his “legal, professional or occupational status” and when the victim is “on probation or parole, or is detained in a hospital, prison or other institution____” Defendant was a corrections officer at the Salem County Jail, where the victim was incarcerated on a detainer from the Immigration and Naturalization Service. Under those circumstances, intercourse itself is the crime, and here the proof of intercourse was strong, the verdict clearly sustainable even without the evidence challenged in this appeal. We find, however, as did the Appellate Division, that evidence was improperly admitted, and we cannot say that it was harmless. The admissibility of the evidence and harmless error were the only two points asserted in the State’s petition for certification following the Appellate Division’s reversal of the conviction. State v. Spann, 236 N.J.Super. 13, 563 A.2d 1145 (1989).

As noted above, the only real issue, given the nature of the crime, was whether defendant had intercourse with the prisoner. Consent, force, or threats are irrelevant under the offense that was charged. The challenged evidence was that defendant was the father of the victim’s child, conception clearly having occurred while she was imprisoned. If he-was the father, criminal intercourse had occurred. The evidence consisted of blood and tissue tests, including human leukocyte antigen (HLA) tissue tests used to prove not that defendant was or was not excluded as the father but that he was the father. The specific item of that proof objected to by counsel was the State expert’s opinion, based on those tests, that the “probability” of defendant’s paternity was 96.55%. Obviously, that probability opinion, if improperly admitted, was highly prejudicial. If the expert’s opinion were credited by the jury, unusually strong contradictory evidence would be required to overcome it. The expert’s qualitative description of the percentage, expressed in non-mathematical terms (known as the “verbal predicate”), was that it was “very likely” defendant was the father. As stated by the prosecutor in summation, “guilt ... is proved to a mathematical certainty ... by carefully applying an objective scientific technique to the hard facts of this case.”

The expert, testifying that the probability of defendant’s paternity was 96.55%, knew absolutely nothing about the facts of the case other than those revealed by the blood and tissue tests of defendant, the victim, and the child, and that defendant was the accused.

I

Use of Blood-Tissue Specimens to Prove Paternity; Calculation of Probability of Paternity; Use of Calculation in this Case

Until relatively recently, blood-grouping tests to establish paternity were admissible only to exculpate the accused in paternity cases. N.J.S.A. 2A:83-3 (repealed by New Jersey Parentage Act, L. 1983, c. 17, § 23). Science had proven, and there is apparently no question about the validity of the proposition and certainly none raised in this case, that certain blood specimens completely exclude others. Thus, blood specimen “X,” found at the scene of the crime and presumably that of the criminal, cannot come from an accused who has blood specimen “Y.” Similarly, blood specimens from mother and child that conclusively determine that only a man with blood specimen “X” could be the father eliminate a man with blood specimen “Y.” In such cases, if the accused’s blood was excluded, he was innocent; in paternity disputes, he was not the father. In New Jersey paternity cases, this limited use of blood tests, to prove only that defendant was not the father, was codified in 1939. R.S. 2:99-3, N.J.S.A. 2A:83-3 (repealed). On the other hand, however, if the blood specimen was of the kind that could have come from the purported father, the evidence was apparently inadmissible to prove paternity.

The lack of probative force of this evidence for the purpose of proving paternity was thought to warrant its exclusion. Its identifying factor, the fact for instance that 50% of the population, including the accused, have blood that could have produced a specimen matching that of the father, was deemed too insignificant to justify admission if offered as independent proof of paternity, i.e., sufficient proof by itself. Even though insignificantly probative, it nevertheless was admissible as “a link in the chain of evidence” in criminal trials, just as the alleged assailant’s blond hair is used against a blond defendant. See State v. Beard, 16 N.J 50, 58-59, 106 A.2d 265 (1954) (holding type O — the victim’s blood type and also the most common type — blood stains on defendant’s clothing admissible as “link in the chain of evidence”); see also State v. Alexander, 7 N.J. 585, 593-94, 83 A.2d 441 (1951) (allowing evidence of defendant’s blood type at murder trial for purpose of showing it was of the same type as blood found on the murder weapon), cert. denied, 343 U.S. 908, 72 S.Ct. 638, 96 L.Ed. 1326 (1952).

With the advent of multiple tests of blood samples, geneticists were sometimes able to exclude up to 72% of the population from certain blood types, i.e. given that kind of sample, those tests conclusively demonstrated that the sample could have come from only a limited portion of the population — 28% of it. Joint AMA-ABA Guidelines: Present Status of Serologic Testing in Problems of Disputed Parentage, 10 Fam. L.Q. 247, 256-57 (1976) [“Joint AMA-ABA Guidelines”]. And with the discovery and development of HLA tissue testing — a test not of blood alone but of tissues of all kinds — the combination of blood and tissue testing, and on many occasions HLA testing alone, very often brought the exclusionary percentage to 95% and higher. Ibid.; D.H. Kaye, Plemel As a Primer on Proving Paternity, 24 Willamette L.Rev. 867, 868 (1988) [“Kaye, Plemel As Primer”}. In contrast to earlier blood-group testing, which had limited utility in identifying rare blood types, the advanced HLA systems enable geneticists to identify a rare blood type “in virtually every case.” Robert W. Peterson, 4 New Things You Should Know About Paternity Tests (But Were Afraid to Ask), 22 Santa Clara L.Rev. 667, 675 (1982) [“Peterson, Paternity Tests”}.

When the portion of the population excluded ran as high as, e.g., 98%, it became intuitively obvious that if only 2% of the population could produce that sample and defendant was part of the 2%, it was not only consistent with his guilt, but tended to prove it — here that he was the father. Tests of blood and tissue samples started to be admitted not only to prove exclusion but also to prove paternity. See Essex County Welfare Div. v. Harris, 189 N.J.Super. 479, 482-83, 460 A.2d 713 (App.Div.1983); J.H. v. M.H., 177 N.J.Super. 436, 441, 426 A.2d 1073 (Ch.Div.1980); Malvasi v. Malvasi, 167 N.J.Super. 513, 515, 401 A.2d 279 (Ch.Div.1979). With an estimated one out of every six children born out of wedlock in this country, Kaye, Probability of an Ultimate Issue, supra n. 1, 75 Iowa L.Rev. at 76 n. 5, testimony revealing the probability of paternity becomes important, to society in general and to the welfare system in particular. Prodded by federal laws aimed at identifying fathers for child-support purposes where children received welfare benefits, New Jersey amended its parentage laws, for the first time allowing the court to require blood or genetic tests in contested paternity cases and to compel such tests when requested by a party. N.J.S.A. 9:17-51a. Whenever HLA tests are ordered by the court, they are admissible in evidence to establish “the positive probability of parentage.” N.J.S.A. 9:17-51e. Moreover, “evidence relating to paternity may include ... genetic or blood tests, weighted in accordance with evidence, if available, of the statistical probability of the alleged father’s paternity”. N.J.S.A. 9:17-52.

Precisely that kind of positive proof of paternity was used in this criminal case, as it had been in prior civil paternity cases without objection. See, e.g., Jones v. Jones, 242 N.J.Super. 195, 200, 576 A.2d 316 (App.Div.), certif. denied, 122 N.J. 418, 585 A.2d 412 (1990); Middlesex County Bd. of Social Servs. v. G.G., 237 N.J.Super. 322, 323-34, 567 A.2d 1019 (App.Div.1989). The State’s expert stated that the blood and tissue samples, combined with statistical data reflecting the number of men with the relevant genes, excluded 99% of the North American black male population as possible fathers. In other words,.only 1% of the presumed relevant population had the type of blood and tissue that the father must have had, and further, defendant was included within that 1%.

In calculating a final probability of paternity percentage, the expert relied in part on this 99% probability of exclusion. She also relied on an assumption of a 50% prior probability that defendant was the father. This assumption, not based on her knowledge of any evidence whatsoever in the case, placed the odds of defendant being the father — wholly apart from the blood-tissue test — at fifty-fifty. The fifty-fifty odds are usually expressed as “defendant being no more or less likely of being the father than any other man chosen at random.” The claim of the victim (that defendant is the father) and the claim of the accused (that he is not) ostensibly are given equal weight. Or, as the expert stated in this case, “everything is equal ... he may or may not be the father of the child.” Based on the various tests, and the fifty-fifty assumption, the expert concluded that “[t]he likelihood of this woman and this man producing this child with all of the genetic makeup versus this woman with a random male out of the black population ... [results in] a probability of paternity [of] 96.55 percent.”

This figure was conveyed to the jury to mean what it says— this man is the father, or at least it is 96.55% probable that he is. It is not intended to and does not mean that he is part of a small group who might be the father (1% — and if there are 100.000 men in the relevant population, that “small group” adds up to 1,000 men). It means that even though there may be 1.000 others who fit the bill, he is the father — the odds are not 999 to 1 against the possibility of his being the father, but a 96.55% probability that he is. If credited, the opinion is enormously persuasive.

The expert’s opinion was based on a mathematical combination of three factors: the expert's assumed probability that defendant was as likely as any other man to be the father; the “probability” that a guilty súspect would have the required blood type (the probability here is 1, i.e., 100%, for whoever was “guilty,” namely, the father, must have that blood type); and the probability that any man chosen at random would have that blood type (here 1%). Using a mathematical formula (Bayes’ Theorem) apparently universally-accepted as valid in conventional probability analysis, the expert calculated the probability of paternity by multiplying the assumed odds (fifty-fifty, such odds being expressed as “1”) by the relative likelihood of paternity as shown by the tests, called a “likelihood ratio” and calculated by dividing the probability of the incriminating results being found in a guilty suspect (1.0) divided by the probability that they will be found in an innocent suspect (.01). This multiplication (1 x 1/.01) gives the new odds: 100. Since odds of 100 means a probability of 100 out of 101 chances (odds of 3, for instance, means 3 to 1 or three out of four chances, a probability of .75), the probability thus calculated would be 99.01%. In fact, as noted above, the probability of paternity figure was 96.55%. Essentially, the formula the expert actually used included an exclusionary factor of 3.57% (not 1%) and would look something like the following:

1 X 1= 28 /.0357

(prior (likelihood (new odds) ratio) odds).

The odds of 28 are the equivalent of a probability of 96.55%.

The reports of blood and tissue testing labs fairly regularly use this mathematical formula, calculating the probability of paternity figure based on the fifty-fifty assumption (that assumption sometimes referred to as the “prior probability,” to convey the sense that it is the probability of defendant being the father based'on all of the evidence in the case prior to any consideration of the blood and tissue test evidence). See Richard H. Walker, Guidelines for Reporting Estimates of Establishment, in United States Dep’t of Health and Hum. Servs., Essentials for Attorneys in Child Support Enforcement, app. C, 391, 392 (1986). Many of the experts who testify concerning the lab results also use the fifty-fifty assumption, following Joint Guidelines formulated in 1976 by the American Medical Association (A.M.A.) and the Section on Family Law of the American Bar Association (A.B.A.). Joint AMA-ABA Guidelines, supra, 10 Fam.L.Q. at 262.

On cross-examination defense counsel brought out the fact that the probability of paternity percentage was based on that fifty-fifty assumption. The expert described it as a “neutral” assumption. Since it supposedly favored neither the accused nor the victim, the expert said it gave the contention of each side (mother and purported father) equal weight and eliminated any subjectivity from the opinion. Her characterization of the evidence was that its “purely objective” nature was “one of the beauties of the test”; that it “makes no assumption other than everything is equal”; and that “the jury simply has objective information.” According to her testimony, there was no taking of sides, no judgment on the facts of the case. Defense counsel saw it differently. Counsel noted that even if it were conclusively proven that defendant had been out of the country at the time when conception could have occurred, this expert still would have concluded that the probability defendant was the father was 96.55%. Counsel’s observation was correct; the expert’s opinion had no relation whatsoever to the facts of the case.

The Appellate Division ruled that the probability of paternity percentage was inadmissible to prove intercourse because, in that court’s view, the calculation itself assumed that intercourse had taken place. 236 N.J.Super. at 26, 563 A.2d 1145 (citing State v. Hartman, 145 Wis.2d 1, 426 N.W.2d 320, 326 (1988)). Quite simply, the Appellate Division ruled that the State cannot prove intercourse through a formula that assumes intercourse, or put differently, the trier of fact cannot convict a defendant of a crime through a formula that assumes the defendant committed the crime. Ibid. That conclusion, supported by language in some cases, e.g., In re Paternity of M.J.B., 144 Wis.2d 638, 425 N.W.2A 404, 409 (1988); County of Sonoma v. Grant W., 184 Cal.App.3d 868, 872, 229 Cal.Rptr. 297, 301, judgment vacated, 187 Cal.App.3d 1439, 232 Cal.Rptr. 471 (1986); Everett v. Everett, 150 Cal.App.3d 1053, 1064, 201 Cal.Rptr. 351, 362-63 (1984); People v. Pasko, 184 Ill.App.3d 528, 132 Ill.Dec. 722, 726, 540 N.E.2d 462, 466 (1989), as well as by statements in articles on the subject, e.g., Peterson, Paternity Tests, supra, 22 Santa Clara L.Rev. at 685, was almost compelled by the record in this case — the expert practically conceding the point and both counsel agreeing that intercourse was assumed in the calculation.

The conclusion, however, is incorrect. The .5 prior-probability assumption (odds of 1) says only that the chance that defendant is the father is fifty-fifty, that it is just as likely that he is not the father as that he is, or that it is just as likely that he is as that any man chosen at random is. Those odds, for instance, are wholly consistent with a fact pattern that one and only one man had access to and intercourse with the victim and that one of two, and only two, men, including defendant, could possibly have been that one man, neither one more likely than the other to be the father. The fifty-fifty odds calculated into the probability of paternity percentage do not at all assume that defendant had intercourse with the victim; indeed, defendant might have been the one with no access to the victim. See Kaye, Probability of an Ultimate Issue, supra, 75 Iowa L.Rev. at 105 n. 153 (noting .5 prior probability “does not assume that intercourse definitely took place”); Mark Ellman & David Kaye, Probabilities and Proof: Can HLA and Blood Group Testing Prove Paternity?, 54 N.Y.U.L.Rev. 1131, 1150 (1979) [“Ellman & Kaye, Probabilities and Proof”] (stating fifty-fifty assumption “equivalent to supposing that the universe of possible fathers is already reduced to two equally likely suspects before considering the HLA test results.”). Those odds say only that the chances are fifty-fifty that he is the father. Obviously, they assume a substantial possibility, 50%, that he had intercourse with the victim, but not that he positively did.

But even on that correct understanding of the effect of the fifty-fifty assumption, a defendant could justly argue that it is totally unfair, indeed inadmissible, to ascribe even that substantial probability — 50%—to him, without the slightest regard to the facts of the case.

II

Enabling Jury to Use Its Own Estimate of Guilt Along with Expert’s Calculations of Probability of Paternity

For different reasons, however, we agree that the admission of the probability of paternity opinion as presented in this case was error. Although the jury learned, in cross-examination of the expert, of the expert’s assumption of a 50% prior probability that defendant was the father, the clear impression given by the expert was that it was somehow a “scientific” assumption, an accepted part of a scientific calculation, “objective,” “neutral,” “fair.” It is no such thing — although it is often, indeed apparently almost regularly, used by forensic experts testifying in paternity matters. See Mikel Aichin, Some Fallacies in the Computation of Paternity Probabilities, 36 Am.J.Hum.Genetics 904, 906, 915 (1984) [“Aichin, Fallacies ”] (asserting that although most paternity testers accept mathematical framework underlying probability of paternity percentage, courts have gone too far in accepting this expert testimony). While counsel could have demonstrated this inherent lack of neutrality through fuller cross-examination, we think that his objections to the introduction of the probability of paternity percentage on that ground were well founded, fairly clearly stated, and should have been sustained.

More than that, we conclude that even if not objected to sufficiently by counsel, the expert’s opinion on probability of paternity did not satisfy the most fundamental requirement of expert testimony: its ability to aid the jury in its deliberations. See State v. Kelly, 97 N.J. 178, 209, 478 A.2d 364 (1984). Moreover, as presented, the testimony “create[d] [a] substantial danger of ... misleading the jury.” Evid.R. 4; see also Fed.R.Evid. 403 (requiring exclusion of evidence where probative value “substantially outweighed by the danger of ... misleading the jury”). In this criminal case, the jury had no idea what to do with the probability of paternity percentage if its own estimate of probabilities (the prior probability of paternity as estimated by the jury apart from blood and tissue tests) was different from .5. There was neither guidance from the expert nor specific instructions from the trial court regarding this crucial aspect of the probability of paternity opinion. Was the jury supposed to reject the expert’s opinion, or was that opinion still of scientific value because of its alleged “objectivity”? Was the expert’s opinion valid even if the jury disagreed with the assumption of .5? If the jury concluded that the prior probability was .4 or .6, for example, the testimony gave them no idea of the consequences, no idea of what the impact (of such a change in the prior probability) would be on the formula that led to the ultimate opinion of probability of paternity.

The jury did not know, for instance, that even if it believed that the prior probability was half of the assumed prior probability, namely, .25 instead of .5, the formula would not at all result in cutting in half the ultimate result, the probability of paternity percentage. Indeed, it would still have left the probability of paternity above 90% (the reduction apparently being from 96.55% to 90.24%). This total lack of “neutrality” on the part of the assumption could not be understood without that kind of information, which would have given the jury at least some basis for evaluating the significance of its own prior-probability determination, assuming it made one. Additionally, a full exposition of the impact of differing prior-probability assumptions would have aided the jury in evaluating the validity and usefulness of the formula itself as applied to paternity' cases.

There is no contention in this case by defendant that the probability of paternity thus computed is inadmissible as such (at oral argument defense counsel said that the probability of paternity opinion was admissible if the jury itself found that the prior probability was .5). We therefore could conclude this opinion with the implicit holding above, namely, that a probability of paternity opinion is admissible but only if the expert notes that the calculations leading to that opinion use as one of the critical factors an assumed prior probability of paternity of .5. While this .5 assumed prior probability clearly is neither neutral nor objective, rather than prohibiting an expert witness from describing it as such, we would leave it to counsel to challenge this characterization through cross-examination. However, a jury should be required to use its own estimate of the prior probability of paternity, one based on all of the evidence in the case other than the scientific evidence arising from the blood and tissue tests; a prior probability, in other words, based on facts of which the expert has absolutely no knowledge — the facts of the case as they would exist were there no scientific tests, no scientific reports, and no expert. Furthermore, the expert’s testimony should be required to include an explanation to the jury of what the probability of paternity would be for a varying range of such prior probabilities, running, for example, from .1 to .9.

On this last point, we note that a similar approach, initially suggested by Professors Ellman and Kaye, Probabilities and Proof supra, 54 N.Y.U.L.Rev. at 1152-58, has been adopted by the Supreme Court of Oregon. Plemel v. Walter, 303 Or. 262, 735 P.2d 1209, 1219 (1987). In that case, the court held that an expert who testifies regarding a probability of paternity “should present calculations based on [varying] assumed prior probabilities of 0, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 percent.” 735 P.2d at 1219. Such an approach ensures that the jury’s attention will be focused on the other evidence in the case and that it will not be misled by the expert’s assumption of a prior probability of .5. Ibid.; see generally Kaye, Plemel As Primer, supra, 24 Willamette L.Rev. 867.

Other courts have challenged the use of the fifty-fifty assumption. See, e.g., County of Sonoma v. Grant W., supra, 184 Cal.App.3d at 868, 229 Cal.Rptr. at 301-302; Everett v. Everett, supra, 150 Cal.App.3d at 1070, 201 Cal.Rptr. at 361; Commonwealth v. Beausoleil, 397 Mass. 206, 490 N.E.2d 788, 797 n. 19 (1986); Kofford v. Flora, 744 P.2d 1343, 1351-52 (Utah 1987); Bridgeman v. Commonwealth, 3 Va.App. 523, 351 S.E.2d 598, 603 (1986); In re Paternity of M.J.B., supra, 425 N.W.2d at 409. Indeed some courts have rejected the use of the probability of paternity statistic altogether on the grounds that the assigned .5 prior probability renders the statistic unreliable. E.g., Plemel v. Walter, supra, 303 Or. 262, 735 P.2d at 1219; Cole v. Cole, 74 N.C.App. 247, 328 S.E.2d 446, 450-51 (1985), aff'd 314 N.C. 660, 335 S.E.2d 897 (1985); People v. Pasko, supra, 132 Ill.Dec. at 727, 540 N.E.2d at 467; Sara H. v. Bart D., 121 Misc.2d 425, 432, 467 N.Y.S.2d 1001, 1005 (Fam.Ct.1983).

In this somewhat abstruse area, therefore, procedures should be designed to avoid an outcome based on an unchallenged and unexplained .5 assumption of prior probability — unexplained and unchallenged because of the possible lack of knowledge of counsel. And these procedures should also obviate a jury unenlightened concerning the impact, on the probability of paternity opinion, of varying prior probabilities. Other problems, such as the possibility of error in the lab tests, are common to all similar expert testimony and presumably will be brought out in cross-examination as they were here.

Ill

Admissibility of Probability of Exclusion and Paternity Index Based on Defendant’s Blood-Tissue Type

Given the controversies that exist concerning this matter— the admissibility not only of the probability of paternity opinion, but of the exclusionary percentage itself, as well as suggested conditions required in other cases that must be satisfied before such evidence is admitted, see, e.g., Commonwealth v. Beausoleil, supra, 490 N.E.2d at 795-97; Kofford v. Flora, supra, 744 P.2d at 1353 — we believe further comment is needed. The comment is intended for consideration by courts (and attorneys) facing these issues but is not intended to be binding unless explicitly indicated. Our observations are based on cases, texts, and articles that in other contexts might be adequate to anticipate and dispose of related problems without a comprehensive record before us in a specific case — and the record here is far from comprehensive. Those sources, however, not only disclose raging controversy but demonstrate a subject matter that, at certain levels, is so complex that we are reluctant to categorically dispose of the issues in the absence of a comprehensive adversarial proceeding, and especially so in the context of a criminal case. We therefore leave the initial determination of all of these issues — including the admissibility of the probability of paternity and appropriate conditions on its admissibility — to trial courts when these issues are presented and fully tried. Our comments are intended solely as guides and considerations, none of these matters having been briefed or argued before this Court. We provide this guidance because the questions involved will inevitably arise in future cases of this kind, including some criminal cases other than rape prosecutions, e.g., when blood and tissue type of defendant corresponds to type found at scene of crime.

We note that the Appellate Division, in ruling on the admissibility of the probability of paternity opinion, properly ruled only on the propriety of the expert’s assumption of a 50% prior probability. 236 N.J.Super. at 27, 563 A.2d 1145. It did not become involved, and did not have to, with the question of whether that defect in the expert’s testimony, if corrected, would have rendered the probability of paternity opinion admissible, and, if so, under what conditions. Furthermore, its observations concerning the admissibility of other evidence— the exclusionary percentages and the related paternity index— were dictum, id. at 25, 563 A.2d 1145, because both parties agreed they were admissible. This dictum, with which we agree, requires further explanation.

We explicitly note here that in addition to the probability of exclusion, the related paternity index — if that has been calculated — is admissible at trial. It is, in effect, an exclusionary percentage that is based on additional blood tissue information resulting in a different likelihood ratio — usually higher than it would be without that information. Kaye, Probability of an Ultimate Issue, supra, 75 Iowa L.Rev. at 89-91. As we understand it, the exclusionary percentage, calculated by reference to a table of frequencies among the relevant population, is the result of the battery of tests that are usually made on a blood-tissue specimen. Each test is presumed to be independent of the other, the net result being not simply the exclusionary percentage that results from a particular test, but the exclusionary percentage that results from all of them, one being multiplied by the other. The “paternity index” adds another element: it factors into the exclusionary percentage (which discloses the percent of the population that has the required blood-tissue type) the relative likelihood of that type being transmitted to the child, some blood-tissue types included within the 1% being more likely to be transmitted than other included types. In other words, the less refined exclusionary percentage reflects the fact, for example, that only one out of a hundred men within the relevant population have the blood-tissue type that the father must have. In a population of one million there are presumably 5,000 such men, any one of whom could be the father. Refining the blood-tissue type genetic analysis further, we learn that there are sub-types and that while any one of the 5,000 could possibly be the father, those within that group who have a certain sub-type are more likely than others to be, this greater likelihood being statistically measurable in having the effect of increasing the exclusionary percentage and the likelihood ratio. (Some sub-types within the 5,000 are less likely to be the father, and result in a lower likelihood ratio.) The paternity index is essentially this new likelihood ratio. Kaye, Plemel As Primer, supra, 24 Willamette L.Rev. at 871-73.

The question of the permissible use of this kind of evidence is similar to that posed in Landrigan v. Celotex, 127 N.J. 404, 414, 605 A.2d 1079 (1991). There, as here, the evidence consisted of two distinct elements: first, the non-statistical evidence (the decedent’s exposure to asbestos, and the absence of other potential causative factors) indicating that asbestos might have caused colon cancer — all of that evidence comparable to the non-scientific evidence in this case tending to prove that intercourse occurred; and second, background associative factors— that it is more likely (in Landrigan, 1.55 was the likelihood ratio) that one exposed to asbestos will get colon cancer than one who is not — this statistical element of the case comparable to the evidence in this case of the greater likelihood that a man with a blood-tissue type of the defendant is 100 times more likely to be the father than a man chosen at random.

In Landrigan, we concluded, that the epidemiological evidence — the statistical likelihood that asbestos might have been the cause based solely on the greater occurrence of colon cancer in those who are exposed to asbestos — could be used along with other non-statistical “direct” evidence to support a conclusion of causation. In this case, instead of simply giving the jury both sets of facts — the underlying facts of the case and the related statistical evidence — and leaving to the jury the determination of the significance when both sets are put together, as we did in Landrigan, here a mathematical computation is added to the mix, one that purports precisely to calculate the probability of the ultimate issue. The point here is that there is nothing fundamentally new in the use of blood-tissue tests to support the conclusion of paternity. What is new is the question of the admissibility of this mathematical formula to guide the jury in its use of the test information.

IV

General Admissibility of Expert’s Mathematical Calculation of Probability of Paternity

Because the issue was neither tried nor raised before us, we do not decide whether the probability of paternity opinion, based on Bayes’ Theorem, is sufficiently reliable to warrant its use in criminal cases to prove paternity. Its use in civil paternity proceedings appears to have legislative authorization. See N.J.S.A. 9:17-52c (permitting evidence “of the statistical probability of the alleged father’s paternity”). Opinions based on Bayes’ Theorem, however, are far from universally accepted for forensic purposes, especially in criminal cases. As noted below, we leave the determination of the admissibility of the probability of paternity opinion to the trial court after a full hearing of the matter.

Without meaning to foreclose examination of any issue that the trial court deems relevant in making the admissibility determination, we suggest that the precise issue is rather narrow. We believe, from our readings, that Bayes’ Theorem, when applied in conventional probability analysis, is practically universally accepted as valid — certainly sufficiently accepted to conform to any requirement of “general acceptance in the relevant scientific community.” See Probability and Inference in the Law of Evidence ix (Peter Tillers and Eric D. Green eds., 1988) (“[E]ven the most rigorous critics of Bayesianism do not argue that Bayes’ Theorem is invalid”); Peterson, Paternity Tests, supra, 22 Santa Clara L.Rev. at 682 (“there is no dispute over the mathematical correctness of Bayes’ Theorem”). What is not at all clear is its general acceptance for the purpose of converting what is essentially a non-mathematical conclusion of a prior probability of guilt into a higher probability through the use of the formula.

The controversy, rather than the “general acceptance,” concerning the use of the probability of paternity opinion and Bayes’ Theorem or formula — indeed the evidentiary use of Bayes’ Theorem at all — is best reflected in the scholarly articles on this issue. See generally D.H. Kaye, Presumptions, Probability and Paternity, 30 Jurimetrics J 323 (1990); C.C. Li & A. Chakravarti, An Expository Review of Two Methods of Calculating the Paternity Probability, 43 Am.J.Hum.Genet ics 197 (1988); L. Jonathan Cohen, The Role of Evidential Weight in Criminal Proof, 66 B.U.L.Rev. 635 (1986); Lea Brilmayer, Second-Order Evidence and Bayesian Logic, 66 B.U.L.Rev. 673 (1986); Stephen Fienberg & Mark J. Schervish, The Relevance of Bayesian Inference for the Presentation of Evidence and for Legal Decisionmaking, 66 B.U.L.Rev. 771 (1986); Leonard J. Jaffee, Of Probativity and Probability: Statistics, Scientific Evidence, and the Calculus of Chance at Trial, 46 U.Pitt.L.Rev. 925 (1985); Craig R. Callen, Notes on a Grand Illusion: Some Limits on the Use of Bayesian Theory in Evidence Law, 57 Ind.L.Rev. 1 (1982); Michael O. Finkelstein & William B. Fairley, A Bayesian Approach to Identifi cation Evidence, 83 Harv.L.Rev. 489 (1970). The intensity and complexity of the dispute is mind boggling on occasion for those other than mathematical experts. Indeed, even the experts have difficulty with it. One, for instance, referred to the Bayes’ Theorem in 1987 as the “reigning” view, D.H. Kaye, Apples and Oranges: Confidence Coefficients and the Burden of Persuasion, 73 Cornell L.Rev. 54 (1987), but five years earlier had described it as “not used as widely as the classical theories.” D.H. Kaye, The Numbers Game: Statistical Inference in Discrimination Cases, 80 Mich.L.Rev. 833, 853 (1982). This same authority, Professor Kaye, although apparently supportive of the use of the formula to establish probability of paternity in 1979, Ellman & Kaye, Probabilities and Proof, supra, 54 N.Y.U.L.Rev. at 1149, expressly suggested its exclusion in criminal cases in 1987, D.H. Kaye, The Admissibility of Probability Evidence in Criminal Trials, 27 Jurimetrics J. 160, 172 (1987).

The disagreement on the subject is such as to prevent us from reaching any conclusion about “general acceptance.” What is needed is what the trial court will have: examination and cross-examination on that issue. It boils down to this: you have a mathematical formula that invariably works in converting a mathematical statistical probability into a new probability by using in that formula new information about the matter, here the likelihood ratio based on the blood-tissue tests. The question is whether the formula produces reliable results when it is applied to a jury’s conclusion about the prior probability— for instance when a jury, let us say in this case, concludes that even without the blood-tissue tests it believes defendant is guilty, that he is the father, and it quantifies that belief by saying that it is 60% probable that he is the father. Ordinarily, a 60% probability means that out of ten chances, the event in question will occur six times, but not the four other times. But what does a 60% probability mean in this case other than the strength of the jury’s belief in guilt? That is just the beginning of the argument.

One of the ends of the argument is the meaning of the ultimate figure — here that the probability of paternity is 96.-55%. The expert translates that into “very likely,” based on the verbal predicate set forth in the Joint AMA-ABA Guidelines. Joint AMA-ABA Guidelines, supra, 10 Fam.L.Q. at 262. To a layman, 96.55% probability seems to correspond to something much stronger, highly likely, almost certain. But how is the jury to relate that percentage to the governing standard: “beyond a reasonable doubt”?

The formula is helpful, if one considers it helpful, because it tells the jury in mathematical terms just how strongly the blood-tissue tests may be deemed to point in the direction of paternity — here, converting an assumed probability of 50% into one of 96.55%. If valid, the expert’s opinion performs a service in helping the jury in such a case, for jurors presumably will have great difficulty in figuring out the significance of the likelihood ratio. Put differently, although the jury will intuitively and logically understand that the exclusion of 99 out of every 100 males as possible fathers increases the likelihood that defendant is the father, the jury will have difficulty in assessing just how much that likelihood is increased. The need for help in making that assessment is underscored when the typical arguments about the exclusionary percentage are considered— arguments so often made that one writer calls them “the prosecutor’s fallacy” and “the defense attorney’s fallacy.” William C. Thompson & Edward L. Schumann, Interpretation of Statistical Evidence in Criminal Trials, The Prosecutor’s Fallacy and the Defense Attorney’s Fallacy, 11 Law & Hum.Behav. 167, 170-72 (1987). The argument often made or implied by the prosecutor is that because there is only one chance in a hundred that the defendant would have this blood type if he were not the father, the jury may conclude that there must be a 99% chance that he is the father. The defense attorney’s argument is that if one out of every 100 men has this blood-tissue type, then because the city where the crime occurred has one million people, there are presumably 10,000 people with that same type, 5,000 of them men — and the odds against defendant being the father are therefore 4,999 to 1. The defense argument, according to one study, is found more persuasive than the prosecutor’s. Id. at 171. The conflict between the two arguments shows the jury’s need for help in evaluating the significance of the exclusionary percentage. That need provides the justification and reason for the admission of the opinion and calculation of probability of paternity.

For all of these reasons, the trial court should conduct an Evidence Rule 8 hearing, determining the expert’s qualifications and the satisfaction of the conditions attached to the admission of expert testimony, i.e., “general acceptability” (see Rubanick v. Witco Chemical Corp. 125 N.J. 421, 454, 593 A.2d 733 (1991)). The court may also decide that an Evidence Rule 4 hearing is needed. Its purpose would be to determine if the value of the probability of paternity opinion is substantially outweighed by the amount of time it will take to develop it, or the danger of prejudice or confusion.

Ordinarily, the conclusion that allows expert testimony in the first place — here “general acceptability” — is for the court. Furthermore, once it is made, depending on the circumstances, it can become the law for all future cases. We not only do not submit the question of the reliability of the breathalyzer to the jury, it is no longer even submitted to the court in a Rule 8 hearing. We would assume, but we are not certain, that if the trial court’s Rule 8 hearing is comprehensive, that its determination of admissibility, if upheld on appeal, would have a similar effect, permitting the use of Bayes’ Theorem in a criminal case involving the question of paternity in future cases. It is impossible, however, for us to conclude just how much of the conflicting evidence about the validity of Bayes’ in such application should be submitted to the jury. The answer to that question may bear directly on whether a Rule 4 determination is needed, for it seems to us that if the admission of this evidence because it has achieved “general acceptance” nevertheless requires, as a matter of fairness, a two-day trial before a jury to allow the testimony of those who do not accept it, the potential of confusion and the consumption of time may argue against its admission. We distinguish here between the time consumption and lengthy presentation of technical evidence before the court in the Rule 8 hearing (in most cases irrelevant to the Rule 4 question, which is directed at proceedings before the jury) and the same factors as applied to the jury trial itself.

Since we have visited the subject fairly recently (Windmere, Inc. v. International Insurance Co., 105 N.J. 373, 386, 522 A.2d 405 (1987); Landrigan, supra, 127 N.J. at 414, 605 A.2d 1079; Rubanick, supra, 125 N.J. at 433-34, 593 A.2d 733), we need only summarize the rules governing the admission of expert testimony. In New Jersey, the “general acceptance by the relevant scientific community” test, established in Frye, substantially is still the law in New Jersey. See Frye v. United States, 293 F. 1013, 1014 (D.C.Cir.1923); State v. Kelly, 97 N.J. 178, 210, 478 A.2d 364 (1984). But cf. 1 McCormick on Evidence § 203, at 871-72 (4th ed. 1992) (noting that Frye test has lost much of its force); Fed.R.Evid. 702 (permitting admission of expert opinion if it assists trier of fact); Fed.R.Evid. 704(a) (allowing expert testimony on ultimate issue). Despite invitations to do so, this Court has explicitly declined to part from the general acceptance requirement, Windmere, supra, 105 N.J. at 386, 522 A.2d 405, and presumably given a criminal case, would be even more reluctant. See State v. Johnson, 42 N.J. 146, 171, 199 A.2d 809 (1964) (requiring reliability of expert opinion evidence to be “clearly established”).

An exception to the “general acceptance” standard is found in toxic tort cases on the issue of causation. Landrigan, supra, 127 N.J. at 414, 605 A.2d 1079; Rubanick, supra, 125 N.J. at 433-34, 593 A.2d 733. Recognizing the difficulties of proof of causation of cancer, and the apparent injustice of denying all recovery where the proof, although falling short of prior standards, is persuasive, we have allowed expert testimony, even though not generally accepted, where the facts and data relied on are of the kind that comparable experts would rely on, if the methodology or techniques used in converting those facts into an opinion are based on methodology that is similarly recognized by such experts as sound.

The “general acceptance” that is thought to impart sufficient reliability to the expert’s opinion as to warrant its admission is shown through the testimony of experts, through authoritative scientific or legal writings, or through persuasive judicial opinions. State v. Kelly, supra, 97 N.J. at 210, 478 A.2d 364. Our readings, as suggested above, leave us with substantial doubt whether any one of the three methods of demonstrating general acceptance is present here. We know that general acceptance does not mean absolute or universal acceptance, State v. Tate, 102 N.J. 64, 83, 505 A.2d 941 (1986); State v. Johnson, supra, 42 N.J. at 171, 199 A.2d 809, and that total infallibility of the scientific technique is not required. Romano v. Kimmelman, 96 N.J. 66, 80, 474 A.2d 1 (1984). But if the bottom line is general disagreement rather than general acceptance, we doubt if the standard is satisfied.

Clearly, the probability of paternity as derived from indices based on HLA serologic tests and computed with Bayes’ Theorem has achieved considerable recognition in the scientific community. The Joint AMA-ABA Guidelines specifically allow for use of even the fifty-fifty assumption as a “useful working hypothesis,” with the acknowledgement that this assumption “will not correspond to the facts in most cases of disputed paternity.” Joint AMA-ABA Guidelines, supra, 10 Fam.L.Q. at 262. As noted above, there is almost universal support for the now-forensic use of Bayes’ Theorem. Ante at 505-506. “HLA testing is accepted generally in the scientific community as a reliable procedure for proving or excluding paternity.” Commonwealth v. Beausoleil, supra, 490 N.E.2d at 799.

We note also the explicit statutory provision permitting the use of blood and HLA tissue tests to “establish the positive probability of parentage,” N.J.S.A. 9:17-51e, i.e., paternity, in civil paternity cases. That provision also allows “[e]xpert testimony pertaining to these tests,” ibid., suggesting that the probability of paternity opinion used in this matter is statutorily permitted in civil cases, although the statute is not that explicit. The further statutory language allowing “[t]he court, upon application and for good cause shown, [to] limit the admissibility of blood tests or genetic tests,” ibid., effectively safeguards against any potential in civil cases for prejudice arising from test results, presumably including the probability of paternity opinion. Various civil cases, however, seem to assume its admissibility. See, e.g., Essex County Welfare Division v. Harris, supra, 189 N.J.Super. at 482-83, 460 A.2d 713; Jones v. Jones, supra, 242 N.J.Super. at 200, 576 A.2d 316; Middlesex County Board of Social Services, supra, 237 N.J.Super. at 323-24, 567 A.2d 1019.

More than that, the above-cited statutory provision is the result of changes in the federal law designed to increase recovery from fathers failing to support children receiving Aid to Families with Dependent Children (AFDC) payments. The Family Support Act of 1988 (codified at 42 U.S.C.A. §§ 651 to - 69 (1992 Supp.)), requires states to meet minimum paternity establishment performance standards, id. § 652(g)(1), and enhances this capacity by providing improved federal funding for laboratory testing conducted by the states. Id. § 655(a)(1). Under the federal law, states must require “the child and all other parties, in a contested paternity case, to submit to genetic tests upon the request of any such party,” id. § 666(a)(5)(B), except in cases where the applicant or recipient of benefits has “good cause for refusing to cooperate as determined by the State Agency ...” 42 U.S.C.A. § 602(a)(26)(B).

Assuming the validity of this statutory direction in civil cases, see Winberry v. Salisbury, 5 N.J. 240, 244-45, 74 A.2d 406, cert. denied, 340 U.S. 877, 71 S.Ct. 123, 95 L.Ed. 638 (1950), apparently requiring admissibility of the probability of paternity, we would be reluctant to deny the admissibility of expert opinion of genetic testing results in criminal cases simply because the burden of proof is different. Regardless of whether the opinion is offered in a criminal or a civil context, its reliability and its tendency to prove a fact would seem to be the same. It is worth noting that a party in a paternity proceeding (like a defendant in a criminal trial) is entitled to be tried before a jury. N.J.S.A. 9:17-49; R. 5:14-1. Obviously, however, liberty is involved in one case and not in the other. Further‘more, the considerations that prompted the statutory amendment in civil paternity cases may have been deemed to justify either a risk of error or other consequences not acceptable in criminal cases. See Windmere, supra, 105 N.J. at 378, 522 A.2d 405 (“[i]n1;he criminal context, conditions of admissibility must be ‘clearly established’ ”) (quoting State v. Johnson, supra, 42 N.J. at 171, 199 A.2d 809). The quantification of the probability of paternity in the form of a number, while problematic even in a civil case — where we sometimes speak of the burden as “more probable than not,” i.e., more than a 50% probability — causes almost undefinable difficulties in a criminal case, since no one has convincingly equated proof beyond a reasonable doubt with a probability number. L. Jonathan Cohen, The Probable and the Provable 49-57 (1977).

We believe the provision in the statute concerning civil paternity cases, therefore, is persuasive but not at all dispositive of the admissibility of this evidence in criminal cases. Our rules concerning the admissibility of expert testimony must still be satisfied, as well as any special considerations that may pertain to proof in criminal cases. Romano v. Kimmelman, supra, 96 N.J. at 80, 474 A.2d 1; State v. Cary, 49 N.J. 343, 352, 230 A.2d 384 (1967).

Assuming the trial court finds the expert’s calculation of the probability of paternity admissible, we note some questionable restrictions on that admissibility suggested in case law. Several courts have instructed juries that they must disregard a probability of paternity figure unless they first find that the defendant had sex with the mother in the relevant time frame and under circumstances conducive to pregnancy. E.g., Everett v. Everett, supra, 150 Cal.App.3d at 1064, 201 Cal.Rptr. at 361-63; Commonwealth v. Beausoleil, supra, 490 N.E.2d at 797 n. 18; People v. Pasko, supra, 540 N.E.2d at 466. We, however, explicitly reject any notion that intercourse must be proved before the probability of paternity percentage can be admitted, especially where intercourse, not paternity, is the ultimate issue. The calculation — Bayes’ Theorem — if valid, does not depend on any particular degree of confidence in the fact of intercourse.

Some cases have suggested that where the probability of exclusion is under 90%, or the resulting probability of paternity under 95%, the opinion should be excluded. E.g., Commonwealth v. Beausoleil, supra, 490 N.E.2d at 795-96; Kofford v. Flora, supra, 744 P.2d at 1353; see also Imms v. Clark, 654 S.W.2d 281, 287 (Mo.App.1983) (prohibiting admissibility of probability of exclusion where less than 90%). Based on our understanding of the issue, we would reject those limitations. They have no basis in science or in mathematics.

In this case, the expert testified that, based on her interpretation of the Joint AMA-ABA Guidelines, a probability of paternity below 90% would not be useful. In fact, the recommended verbal predicates suggest only estimates below 80% are “not useful,” while the utility of estimates in the 80% to 90% range is “undecided.” Joint AMA-ABA Guidelines, supra, 10 Fam. L. Q. at 262. Nevertheless, if an expert wants to claim that the scientific community has concluded that a probability of paternity that is less than 95% is unreliable or irrelevant, the trial court of course will evaluate that testimony in a Rule 8 hearing. Although we doubt that there will be any such testimony, or that if presented, that it will be persuasive, we note that those proposed conditions show the extent to which the use of the Bayes’ formula is not credited in the courtroom environment. But cf. National Institute of Child Support Enforcement, U.S. Department of Health and Human Services, Essen tials for Attorneys in Child Support 366, 376 (1986) (noting use of Bayes’ Theorem in calculating probability of paternity “is method most familiar to the American court system”).

As a practical matter, the complex issues raised by admitting evidence of HLA test results in paternity and criminal cases are likely to become less and less important, indeed totally irrelevant, once acceptable scientific standards permit a broader forensic use of DNA “fingerprinting.” It is generally accepted that DNA identifying techniques will exclude from consideration the DNA sequences of all but identical twins, making DNA testing the functional equivalent of a fingerprint. Brad R. Byers, Comment, DNA Fingerprinting and the Criminal Defendant: Guilty or Innocent? Only His Molecular Biologist Knows for Sure, 58 Ohio N.U.L.Rev. 57, 58 (1989); Eric S. Lander, DNA Fingerprinting on Trial, Nature 501 (June 1989) . The complexity of the DNA testing procedures, and the apparently largely unregulated practices of those genetic laboratories equipped to conduct DNA testing in criminal cases, raise questions at this time concerning the potential reliability of such evidence in establishing paternity in criminal cases. Leigh C. Lawson, Comment, DNA Fingerprinting and Its Impact Upon Criminal Law, 41 Mercer L.Rev. 1453, 1456 (1990); Peter J. Neufeld & Neville Colman, When Science Takes the Witness Stand, Scientific American 46, 53 (May 1990). But see United States v. Jakobetz, 955 F.2d 786, 799-800 (2d Cir.1992) (affirming admissibility of DNA profiling evidence in criminal cases); Ronald J. Richards, Comment, DNA Fingerprinting and Paternity Testing, 22 U.C.Davis L.Rev. 609, 635-37 (1989) (advocating use of DNA fingerprinting to establish paternity).

V

Use of Probabilistic Analysis in Criminal Trials

The fundamental objections to the use of Bayes’ Theorem to establish probability of paternity are both mathematical and jurisprudential. The mathematical objections are suggested above: they raise doubts about the validity of applying a formula designed for statistical probabilities to an assessment of proofs by the jury that, although it can be expressed as a probability, is in fact simply a statement of the strength, or weakness, of the jury’s belief in a fact, forced into the mold of a statement of probability. The “prior probability” that is the basis for the Bayes’ Theorem calculation is truly no prior probability at all so far as the jury is concerned. Jurors simply believe, at whatever stage of the proceedings they have to make the assessment, that defendant is guilty or not, and have varying degrees, of confidence in that belief. If forced to — and they will be, if Bayes’ Theorem is admitted — they can express that degree of confidence as a “prior probability,” the defendant’s probability of guilt is 80%, 50% or 10%. The question remains whether Bayes’ Theorem, when applied to such a non-statistical probability estimate, is likely to yield reliable results. That is one of the issues the trial court will deal with in its Rule 8 hearing.

The jurisprudential objection is different. It says that even if reliable, this factfinding method should not be used by juries except in the most unusual situations, or where the law explicitly requires a calculation of probabilities. In criminal cases, those objections go beyond the possibility of confusing or overwhelming the jury with mathematical complexities. They go to the heart of the jury’s function — the finding of guilt beyond a reasonable doubt.

These jurisprudential (and other) concerns are set forth in Laurence H. Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 Harv.L.Rev. 1329 (1971). Writing concededly in reaction to a perceived risk at the time that mathematics was about to take over the jury’s factfinding role, Professor Tribe persuasively argued that probabilistic analysis should but rarely be allowed to aid factfinding in criminal trials — and Bayes’ Theorem was very much in mind. Although expressly rejecting a per se exclusion of such evidence, his position comes very close to that. Id. at 1354-55. Some of his arguments, expressed as well by others, must be dealt with.

One argument notes the possibility that the jury will use the associative evidence — the probability of exclusion — twice. First, having heard defendant has the blood-tissue type that the guilty suspect must have and that only one in one hundred have it, the jury will include that fact in its initial assessment of guilt, i.e., in its determination of the prior probability. When Bayes’ Theorem is then applied to that prior probability to reach a conclusion of probability of paternity, the calculation will necessarily again factor in the probability of exclusion, because it is part of the Bayes’ Theorem probability of paternity calculation, impermissibly using the exclusionary percentage twice. Id. at 1366-68.

Second, because Bayes’ Theorem will be introduced in the State’s case and because its use depends on the jury’s prior-probability finding, the jury inevitably will be impelled to focus, during the State’s case, before all of the evidence is in, on the probability of defendant’s guilt. Professor Tribe notes the inconsistency of that result with the presumption of innocence, the jury, of course, required to regard defendant as innocent until found guilty beyond a reasonable doubt. Id. at 1368-71. Simply put, the argument is that the use of that calculation during the State’s case impermissibly violates the jury’s obligation to keep an open mind until all of the evidence is in and deliberations start.

Third, the jury is implicitly asked to find defendant guilty beyond a reasonable doubt even though the probability of paternity itself has a quantifiable element of uncertainty and doubt. Id. at 1375. Stated otherwise, even if the probability of paternity is 95%, does our system of criminal justice encourage a jury to find guilt beyond a reasonable doubt when there is a 5% chance that defendant is innocent?

Finally, the argument notes the counter-intuitive impact of Bayes’ Theorem and the probability of paternity that can result. The ability of the calculation to convert a very low jury estimate based on the facts into an extremely high one after the formula is applied is one such counter-intuitive result. The formula’s ability to declare both the defendant and a suspect (with the same blood type) as each having a 95% probability of being the father is another. With such counter-intuitive results persuasively supported by expert testimony, the fear is the jurors will lose sense of the need to use their intuition, common sense, and sense of community values. Tribe likens the process to a return to trial by battle. Id. at 1376-77.

Although some of these issues, both mathematical and jurisprudential, may ultimately become issues of law for this Court, we prefer to commit their resolution initially to the trial court where they will be subjected to adversarial testing. We are inclined to believe that appropriate jury instructions can cure all of them, or at least diminish their risk to the point that the advantages of the expert’s calculation outweigh these risks, assuming the opinion is otherwise admissible.

Given the guidance of the trial court and the argument of competent counsel, we think juries will be able to cope with the complexities and pitfalls of this kind of probabilistic evidence. Although the dispute on this subject presumably continues, we are not dealing here with some abstruse application of mathematics: the probability of paternity opinion is regularly and routinely used in civil cases and apparently favored if not mandated by both our Legislature and the federal government. The probability of paternity opinion is also routinely used by laboratories that perform this blood-tissue testing. We recognize, however, that if Bayes’ Theorem as applied to blood-tissue testing is admitted in this case, it is presumably admissible in any criminal case involving such blood-tissue testing.

VI

Summary

If the State in a criminal case offers expert proof of the probability of paternity, the trial court should hold a Rule 8 hearing. That hearing should focus on whether the relevant scientific community generally accepts the probability of paternity opinion as a reliable indicator of paternity. The trial court should also inquire concerning the appropriateness of the admissibility of probability of paternity opinions in criminal cases. For while that is ultimately a decision reserved to the court, the differing views on the subject will help expose the issues surrounding this testimony and will aid the court in its determination.

In ruling on admissibility, the trial court should carefully consider the kind of testimony that the jury will hear. For example, if admissibility appears to depend on the validity of applying Bayes’ Theorem to a non-numerical jury assessment of the probability of paternity, the argument and testimony concerning that question of validity may be beyond the understanding of the jury. If that is the case, the trial court will have to determine the consequences — including possibly excluding the opinion or imposing practical limitations on trial testimony concerning the validity issue. Assuming it is concerned with potential confusion and prejudice, the court may, in a Rule 4 hearing, ultimately have to weigh the advantages and disadvantages, the costs and benefits, of the admission of the probability of paternity opinion. This necessarily will require a determination of whether substantially the same benefit — without some of the costs — can be gained through other evidence, e.g., the exclusionary percentage.

If the trial court allows this testimony — the opinion of probability of paternity — other matters, including conditions on its admissibility, should be considered. The expert should be qualified not only as a geneticist but also as a mathematician (which the expert in this case was not); or, alternatively, a mathematician should testify as well as the geneticist concerning the formula. The expert should explain the formula and indicate what it means, but should never be allowed to state that “in my opinion the probability of paternity ...” is a particular percentage. No verbal predicate should be stated in any way, not even a reference to the verbal predicates approved by the Joint AMA-ABA Guidelines (e.g., “very likely,” “likely”). A range of possible prior probabilities should be presented to the jury, along with the probability of paternity applicable to each, resulting from the formula. The jury should be made aware of the formula’s ability, given high exclusionary percentages, to convert low prior probabilities into extremely high probability of paternity opinions. The jury should also be informed, where appropriate, of other counter-intuitive results the formula might produce. And, as in all other cases, the jury should be told that it need not accept the expert’s testimony, that it may reject it either in whole or in part, that it is simply offered to help it in the evaluation of the impact of the blood-tissue evidence and the exclusionary percentage. Finally, the jury must be instructed that the ultimate question — whether defendant, beyond a reasonable doubt, had intercourse with the victim, or, its equivalent in this case, whether defendant, beyond a reasonable doubt, is the father — is for the jury and only the jury to determine; that issue must be determined as stated “beyond a reasonable doubt”; and that no mathematical formulation can relieve it of the obligation to make that determination. The formula, the probability of paternity, all of these things, along with all of the other evidence, are there to aid the jury in its ultimate fact-finding obligation. That obligation, however, does not change.

Some of the above guidelines may be applied to civil cases where paternity is disputed, but we do not intend by this opinion to complicate or make more difficult the accomplishment of the apparent intent of the Legislature, namely, to enable the State or the mother to readily establish paternity through the use of both the exclusionary percentage and the probability of paternity opinion. That issue is not now before us.

In conclusion, we agree with the Appellate Division’s reversal of the conviction: the probability of paternity opinion was improperly admitted as presented in this case. On remand the trial court will decide that issue, if the offer is again made, considering the matters mentioned in this opinion. As for the harmless error argument, it is forceful, for it is almost inconceivable on this record that the jury would find a prior probability of less than 50%. Nevertheless this is a criminal case, and given the novelty of the testimony, the mathematics involved, and the very high estimate of the probability of paternity opinion, we are not satisfied to call its admission harmless error.

We affirm the judgment of the Appellate Division. We remand the matter for a new trial in accordance with this opinion.

For affirmance and remandment — Chief Justice WILENTZ and Justices CLIFFORD, HANDLER, POLLOCK, O’HERN, GARIBALDI, and STEIN — 7.

For opposition — None. 
      
       HLA types correspond to molecules, known as antigens because they react to specific antibodies found in blood as well as on all cells. The production of these antigens is directed by closely-linked genes, known as haplotypes, which are almost always passed as a unit from parent to child and exhibit a substantial number of variations in human population. D.H. Kaye, The Probability of an Ultimate Issue: The Strange Case of Paternity Testing, 75 Iowa L.Rev. 75, 88 (1989) [“Kaye, Probability of an Ultimate Issue"].
      
      To illustrate how the HLA system works in identifying paternity: The child in this case had phenotypes (observable traits corresponding to some set of underlying genotypes) A2 A28 B45 B53, and the mother had HLA types A28 A30 B53 B61. These symbols refer to distinct antigens expressed by genes at two locations (the A locus and the B locus) in the human genome. These two genes, located next to one another on the same chromosome, typically are inherited as a haplotype, one from each parent. Id. at 88. Thus, the child receives one pair of A and B genes from both the mother and from the father. Because the mother and child have types A28 B53, the child must have inherited the haplotype A2 B45 from the father. Any man who did not possess this obligatory haplotype (A2 B45) could be excluded as a possible father. The HLA test showed that defendant’s phenotype was A2 A28 B35 B45, making him a possible father because he possessed the obligatory haplotype. The expert in this case testified that after factoring in the results of the HLA and other blood tests, the probability of exclusion was derived by consulting a table of haplotype frequencies that showed that only 1% of the relevant male population have the inculpatory blood and tissue type, and that the father is found only in that group. Thus, 99% of the relevant male population is excluded and could not be the father.
     
      
       The expert nowhere explained how she specifically arrived at the calculation that led to the "probability of paternity" figure. Our understanding of the mathematics suggests that the actual exclusionary figure used was not 1% but rather 3.57%. Had she in fact used a 1% exclusionary figure, the probability of paternity would have been 99.01%, not 96.55%.
     
      
       The 96.55% probability corresponds to odds of 28 to 1 in favor of defendant being the father instead of the 999 to 1 odds that he is not the father. The 28 to 1 odds correspond to 28 out of 29 chances, a probability of 96.55%.
      Since the incidence of different blood groups, as well as HLA types, varies with race and to a lesser extent geography, gene-frequency tables are derived from population studies of different racial groups. The relevant population considered by the expert in this case was the North American black male population. Unless it was conceded that the father had to be black, it is not clear why such a limitation was used, and the expert’s opinion, as well as most articles on the subject, fails to explain this common practice. In this case there was no prejudice because of the blood and tissue types involved; both the exclusionary figure and the probability of paternity percentage would have been higher if the entire population rather than just the black population had been used.
     
      
       The expert indicated that her results were subject to a sampling error of 3%. Her explanation of the impact of that error, however, was less than complete — indeed, on this record, beyond understanding. She noted that the 1% exclusion rate was based on a sample of 1,900 men, only 19 of them having the type of blood and tissues of a potential father. Conceding the 3% margin of error, she noted that would change the 19 to either 16 or 22 men, depending on which way the error went. But how 3% translates into that difference is impossible to determine. If the correct number were 16, then the exclusionary rate, instead of .01, would be .0084, 16% less than .01, yielding an even greater exclusionary figure and a substantially greater probability of paternity. If the correct number is 22, rather than 19, the exclusionary percentage would be about .0116, rather than .01, a 16% increase, and a correspondingly lower probability of paternity. The margin of error based on sampling, therefore, was acknowledged but on this record not at all adequately explained.
     
      
       Obviously there are other differences between this case and Landrigan concerning the use of expert testimony. In Landrigan, the experts apparently could not have concluded that asbestos was the cause of death without using the epidemiological statistical evidence. In this case, the blood and tissue tests and the accompanying expert opinion based on Bayes’ Theorem are not essential; there is more than sufficient evidence to warrant submission of the case to the jury. What is added, of course, is evidence in the form of an expert’s opinion that not only supports a guilty verdict but, if credited, almost compels it.
     
      
       The statute apparently was enacted six months after New Jersey inadvertently missed the initial deadline for state compliance with new federal welfare requirements. Continued noncompliance would have resulted in the annual loss of an estimated $20 million in federal funds to New Jersey. Paternity Testing Bill Is Sent to Governor, Star-Ledger, May 22, 1990, at 46.
     
      
      
         The individual state welfare agencies are themselves responsible for contracting with “laboratories which perform ... legally and medically acceptable genetic tests which tend to identify the father or exclude the alleged father.” 45 C.F.R. § 303.5(c) (1991). In New Jersey, the Division of Economic Assistance within the State Department of Human Services has established specifications, which the State’s approved testing laboratories are obliged to follow in conducting HLA and other genetic testing. Notification of Award of Annual Contract for Genetic Testing, State of New Jersey, Dep't of Hum. Serv., Div. of Economic Assistance, for Contract Period Nov. 1, 1990, to Oct. 31, 1993. At a minimum, these tests must satisfy the current standards of, inter alia, the Joint AMA-ABA Guidelines. Id. at ¶ 6.1.7(1). As discussed above, these Guidelines recommend the use of the fifty-fifty assumption in calculating the probability of paternity percentage. Joint AMA-ABA Guidelines, supra, 10 Fam.L.Q. at 262.
     
      
       Professor Kaye sharply refutes the merits of these "rules of evidence." Kaye, Probability of an Ultimate Issue, supra, 75 Iowa L.Rev. at 83-87. The particular evidentiary rules imposed by these courts are unlikely to have much effect on the admissibility,of the probability of exclusion, however, because the testing procedures of most laboratories already, on average, exclude more than 90% of the population. Id. at 98.
     