
    STATE of Minnesota, Appellant, v. Troy Bradley BLOOM, Respondent.
    No. C9-94-55.
    Supreme Court of Minnesota.
    April 29, 1994.
    Hubert H. Humphrey, III, Atty. Gen., St. Paul, and Michael 0. Freeman, Hennepin County Atty., Stephen L. Redding, Paul Scoggin, Asst. Hennepin County Attys., Minneapolis, for appellant.
    Patrick J. Sullivan, Asst. Hennepin County Public Defender, Minneapolis, for respondent.
    Hubert H. Humphrey, III, Atty. Gen., Robert A. Stanich, Asst. Atty. Gen., St. Paul, for amicus curiae State of MN.
    Janice M. Symchych, Dorsey & Whitney, Minneapolis, for amicus curiae Inst, of Human Genetics & Mangen Research Assoc., Inc.
    
      Phillip D. Prokopowicz, Asst. Dakota Cty. Atty., Hastings, for amicus curiae MN Cty. Atty’s Assoc.
   OPINION

KEITH, Chief Justice.

Agreeing with the state on the central issue in each of three separate criminal appeals decided today, we hold, first, that the National Research Council’s recent adoption of the conservative “interim ceiling method” for computation of the probability that a randomly selected person would have the same DNA profile as that of a sample of bodily fluids found at a crime scene justifies the creation of a DNA exception to the rule against the admission of statistical probability evidence in criminal prosecutions to prove identity; second, that if the evidentiary foundation provided by the proponent of the evidence is sufficient, a properly qualified expert may express the opinion that, to a reasonable degree of scientific certainty, the defendant is (or is not) the source of the bodily evidence found at the crime scene.

These appeals give this court an opportunity to revisit an issue that recently has been the focus of considerable controversy in the scientific community. The issue is not, as some have put it, the admissibility of DNA identification evidence in criminal prosecutions but the form that the presentation of that evidence takes.

DNA is a long, double-stranded molecule found in chromosomes carried in cell nuclei. William C. Thompson, Evaluating the Admissibility of New Genetic Identification Tests: Lessons from the “DNA War,” 84 J.Crim.L. & Criminology 22, 26 n. 18 (1993). It occurs in all cells that have a nucleus, including white blood cells, sperm cells, cells surrounding hair roots, and cells in saliva. Committee on DNA Tech, in Forensic Science, Nat’l Research Council, DNA Technology in Forensic Science S-l (Prepublication Copy 1992) [hereinafter NRC Report]. Most sections of DNA molecules vary little among individuals within a species. Thompson, supra, at 26 n. 18. However, some sections are polymorphic, meaning they do vary. Id. If two fragments do not match, they could not have a common source, but if they do match, they might have a common source. Id. at 26-27. Researchers as yet have not developed DNA profiles that cannot be shared by two or more people. David T. Wasserman, The Morality of Statistical Proof and the Risk of Mistaken Liability, 13 Cardozo L.Rev. 935, 973 (1991). However, the theory underlying forensic use of DNA profiles is that “as the number and variability of the polymorphisms utilized in the typing procedure increases, the odds of two people having the same profile become vanishingly small.” Id. at 972.

The “vanishingly small” probability figure that experts come up with in case after case is the probability of a random match. Carefully stated, it is the probability that a randomly selected person, if tested, would have the same DNA profile as that of the sample left at the scene. Richard Lempert, Some Caveats Concerning DNA As Criminal Identification Evidence: With Thanks to the Reverend Bayes, 13 Cardozo L.Rev. 303, 305-06 (1991). Thus, when the figure given is 1 in 1 billion, the expert is saying (if the expert chooses words carefully) that there is a 1 in 1 billion chance that a randomly selected person would have the same DNA profile as that of the sample left at the scene. Id.

The basic unmodified approach to obtaining the statistic is to estimate the percentage of people in the population with identical DNA at each particular locus and then, using the so-called product or multiplication rule, to combine the individual frequencies by multiplying them against each other and by the number 2. Thompson, supra, at 69 n. 208. Underlying the use of the product rule is the assumption that the frequency of a match at a particular locus is independent of the frequency of each of the other individual matches against which it is multiplied. NRC Report § 3.2.2, at 3-3.

There are a number of potential sources of error in computing the probability figure. These include:

(a) The databases which one uses may seriously underestimate the frequency in the population of a particular pattern of DNA at a particular locus. Thompson, supra, at 62, 66, 68.

(b) The databases may be unrepresentative, failing to take into account variations among population subgroups, or variations in particular geographical locales, in the frequency of certain DNA patterns at particular loci. Id. at 62.

(c) The assumption of statistical independence may be invalid. Id. at 61-62 n. 174.

If a population survey of Europe showed that 1 of 10 people had blond hair, 1 of 10 had blue eyes, and 1 of 10 had fair skin, one would be wrong to multiply these frequencies to conclude that the frequency of people with all three traits was 1 in 1,000. Those traits tend to co-occur in Nordics, so the actual frequency of the combined description is probably higher than 1 in 1,000.

NRC Report § 3.2.2, at 3-3. The example deals with “expressed” or visible traits, but people do not mate at random and it therefore is possible that the DNA patterns, although “unexpressed,” are not statistically independent either. Lempert, supra, at 311— 12. Indeed, people often mate with other people having the same subset of possible traits, even though the traits are not expressed or visible. Thompson, supra, at 69-70. As stated by Lempert, “evidence of a DNA match is not nearly so probative as people have thought because suspect populations are not random agglomerations with respect to the likelihood of sharing the [traits] compared in DNA analysis.” Lempert, supra, at 312.

(d) The laboratory’s “false positive match rate” affects the reliability of the figure obtained using the product rule. False positive matches do occur, as the result of sloppy laboratory procedures, the poor quality of the materials used, the quality of the DNA sample obtained from the scene, the protocols calling for a match, and human error. Thompson, supra, at 91; Lempert, supra, at 323.

(e) If there was an error in concluding that there was a match at even one band in a particular case, then there is a very real chance that the jury will be told in that case that the chance of a random match is extremely small when in reality there is no match at all.

Because of these factors, the NRC in its 1992 report recommended the use of an extremely conservative “interim ceiling method” for estimating random match probabilities. (It is this method that the state’s expert, Professor Hartl, used in this case to arrive at the 1 in 634,687 figure. See footnote 2, supra.)

One of the concerns expressed in our cases, which we discuss in detail later, has been that admission of the random match probability figure will confuse jurors. There is a chain of inferences that the jurors must make in order to get from the starting point, the testimony as to the probability of a random match, to the conclusion that the defendant is the perpetrator of the crime. Those inferential steps include: match report — true match — source—present at scene' — -perpetrator. See Jonathan J. Koehler, Error and Exaggeration in the Presentation of DNA Evidence at Trial, 34 Jurimetrics 21 (1993). Errors may occur at each step:

(a) The inference that the reported match is a true match. Most expert witnesses are technicians. Andre A. Moenssens, Novel Scientific Evidence in Criminal Cases: Some Words of Caution, 84 J.Crim.L. & Criminology 1, 5 (1993). Forensic scientists typically do not know much about the underlying statistical theory and, even if they do, “are often reluctant to acknowledge^ for example,] that a reported match could be something other than a true match.” See Koeh-ler, supra, at 22. This reluctance is not confined to forensic scientists:

In courtroom testimony, forensic scientists and their academic supporters • often insist that the probability of a false positive is zero- — that is, that false positives are impossible. Although the falsity of these claims has been demonstrated repeatedly, the claims still continue to be made. * * *
Currently, juries often hear nothing about false positives, other than broad assurances that they never occur. * * * [Jjurors hear impressive numbers that appear to quantify with precision the frequency of the DNA profile, accompanied (when the issue is raised at all) by a vague, non-quantitative discussion of the chances of a false positive.

Thompson, supra, at 91-92 (footnotes omitted).

(b) The inference that a true match means defendant is the source. There is nothing inherently wrong in a jury using its inference that the match is a true match as the basis for another inference, specifically, that the defendant is the source. What is important is that the jury know that it has to go through the process of making the inference. The probability that a randomly selected person would have the same profile as the sample found at the scene is not the probability that someone other than the defendant is the source. Koehler, supra, at 27. But it is commonly assumed that it is the probability that someone other than defendant is the source. This is what is often referred to as “source probability error.” Id. In order to give an opinion as to the probability that someone other than defendant is the source, one would first have to estimate the size of the potential source population. Id.

“Source probability errors are frequently committed in the popular press.” Id. at 28; see, e.g., “DNA Data: Letting Jurors Know the Whole Score,” Minneapolis Star-Tribune, Feb. 1, 1994, at 10A (stating that, as the result of a trial judge’s ruling, “jurors will hear testimony on the odds * * * that the DNA evidence against [the defendant] actually belongs to someone else”).

Unfortunately, source probability errors “are also committed by the courts and by experts who should know better.” Koehler, supra, at 28. For example, in a recent case the Eighth Circuit referred to the probability figure as “the probability that someone other than the contributor of the known sample could have contributed the unknown sample.” United States v. Martinez, 3 F.3d 1191, 1194 (8th Cir.1993); see also Koehler, supra, at 28 n. 24 (giving many examples of other courts committing source probability error). Indeed, amicus briefs in this appeal make the same mistake. One can understand attorneys and judges, who are not trained in statistics, making this mistake. And one can understand forensic scientists, most of whom are technicians, making this mistake. But even the best of the scientists make it occasionally.

(c) The inference that defendant was the source means defendant was at the scene. There is nothing inherently wrong in using the inference that defendant was the source to infer defendant was at the scene as long as jurors know that the one does not necessarily follow from the other.

(d) The inferences that defendant was the source and that he was at the scene mean defendant committed the crime. An even more egregious kind of error than “source probability error” is that which has been dubbed “prosecutor’s fallacy,” the fallacious equation of random match probability with the probability that the defendant is the perpetrator of the crime. Koehler, supra, at 31-32. As Koehler says, it really should not be called “prosecutor’s fallacy” because experts, defense attorneys, judges and reporters also sometimes make the mistake; he therefore refers to it as “ultimate issue error.” Id. at 32. One has no way of knowing how often jurors make the error but it is quite possible that such error by jurors is common. Id. Koehler explains, “[A] suspect who actually is the source of the trace may not be the perpetrator of the crime. The suspect may have left the trace innocently either before or after the crime was committed.” Id. at 21-22. Indeed, the use of a person’s bodily fluids to frame that person is not beyond the realm of possibility.

Forensic use of DNA evidence is a very recent development. The first forensic use was in Great Britain less than 10 years ago. Kenneth R. Kreiling, DNA Technology in Forensic Science, 33 Jurimetrics 449, 456-57 (1993). Those who are not by nature skeptical “rushed” to admit the evidence in criminal cases. In the “first wave of cases, expert testimony for the prosecution rarely was countered, and courts readily admitted RFLP findings.” D.H. Kaye, The Admissibility of DNA Testing, 13 Cardozo L.Rev. 353, 357 (1991).

Then law reviews began publishing critical articles dealing with a number of issues, including the standards used for determining individual matches, the adequacy of the studies estimating the frequency of individual traits in the population, the validity of the assumption of independence, the possibility of false matches, and the misleading presentation of things such as random match probability and the possibility of false matches. Unfortunately, the FBI and others advancing the “cause” of the easy admission of DNA evidence have not always behaved admirably.

Because of all the criticism, a Committee on DNA Technology in Forensic Sciences was formed by the National Research Council. The committee’s report, which we referred to earlier, was released in 1992. For an excellent summary of the report, including the committee’s conclusions and recommendations, see Kreiling, supra, at 449.

The NRC report has not put an end to the controversy. Indeed, it appears that the FBI is sufficiently concerned about the response of courts and critics to the NRC report that it has agreed to fund a new study by the NRC in the hope that that will help end what former-FBI Director Sessions called a “crisis.” Thompson, supra, at 82; see footnote 3, supra.

While Minnesota was one of the first courts to admit DNA identification evidence in criminal trials, we took the cautious approach in doing so, insisting that the new forensic techniques receive adequate scrutiny and insisting that proper procedures be followed if the evidence is to be admitted. Thus, in State v. Schwartz, 447 N.W.2d 422 (Minn.1989), we held, inter alia, that (a) because forensic DNA typing has gained general acceptance in the scientific community, DNA test results are admissible if performed in accordance with appropriate laboratory standards and controls and (b) in order to ensure a fair trial, the test data and methodology must be available for independent review by the opposing party. In State v. Nielsen, 467 N.W.2d 615, 619 (Minn.1991), we said that “the day may soon come” when there will be no need in a particular case for a hearing out of the jury’s presence to determine if the foundation for expert DNA testimony has been established. Then, in State v. Jobe, 486 N.W.2d 407 (Minn.1992), we held (a) that the FBI’s internal audit of its DNA RFLP testing procedures sufficiently complied with accepted standards and guidelines, and (b) that the pretrial admissibility hearing should focus only on the testing laboratory’s compliance with appropriate standards and controls, not on the basic reliability of DNA RFLP testing procedures. See also State v. Johnson, 498 N.W.2d 10 (Minn.1993). A reading of these cases makes it clear that we do not, nor have we ever, questioned the theory of human genetics underlying DNA testing and the basic validity of DNA analysis.

As we said at the outset of this opinion, the issue in this case is not the admissibility of DNA evidence but the form that the presentation of the evidence takes. Heretofore, in answering this question, we have applied the so-called Kim rule.

The Kim rule is the rule that emerged from three cases: State v. Carlson, 267 N.W.2d 170 (Minn.1978), State v. Boyd, 331 N.W.2d 480 (Minn.1983), and State v. Kim, 398 N.W.2d 544 (Minn.1987).

The issue in Carlson was whether the trial court erred in allowing an expert to express the results of microscopic hair comparisons in terms of statistical probabilities. One expert, Strauss, testified that the “foreign” hairs found on the victim were similar to the defendant’s hairs in all 15 categories of microscopic comparison, and another expert, Gaudette, testified that the hairs were similar in all 26 categories of comparison he used. We upheld the admission of that testimony but held that the trial court erred, albeit nonprejudicially, in allowing Gaudette to express his opinion of the estimated statistical probability (1 in 4,500) that the foreign hairs were not defendant’s hairs. We said:

Testimony expressing opinions or conclusions in terms of statistical probabilities can make the uncertain seem all but proven, and suggest, by quantification, satisfaction of the requirement that guilt be established “beyond a reasonable doubt.” See, Tribe, Trial by Mathematics, 84 Harv.L.Rev. 1329. Diligent cross-examination may in some cases minimize statistical manipulation and confine the scope of probability testimony. We are not convinced, however, that such rebuttal would dispel the psychological impact of the suggestion of mathematical precision, and we share the concern for “the substantial unfairness to a defendant which may result from ill conceived techniques with which the trier of fact is not technically equipped to cope.” People v. Collins, 68 Cal.2d [319] 332, 66 Cal.Rptr. [497] 505, 438 P.2d [33] 41 [ (1968) ].

267 N.W.2d at 176 (footnote omitted).

Boyd was a pretrial state’s appeal, in a statutory rape ease, of the trial court’s suppression of expert testimony by Dr. H.F. Polesky, M.D., that (a) the chance was 1 in 1,121 that a randomly selected man would have, as the defendant did, all the appropriate genes to have fathered the child that allegedly resulted from the rape and (b) the probability was 99.911% that the defendant was the father of the child. Dr. Polesky obtained these figures by comparing the blood types of the complainant mother of the child, the child and the defendant with respect to 15 different but not highly polymorphic gene systems and by then using the product rule in obtaining the ultimate statistical probability of paternity. In our opinion we stated:

Professor Tribe admits in his article that statistics can be of aid in dealing with matters that are objectively verifiable in the world outside the courtroom, like identification * * *. Thus, he states in dealing with hand-print evidence:
By itself, of course, the “one-in-a-thousand” statistic is not a very meaningful one. It does not * * * measure the probability of the defendant’s innocence — although many jurors would be hard-pressed to understand why not. * * * [E]ven if there were as few as one hundred thousand potential suspects, one would expect approximately one hundred persons to have such prints; if there were a million potential suspects, one would expect to find a thousand or so similar prints. Thus the palm print would hardly pinpoint the defendant in any unique way.
To be sure, the finding of so relatively rare a print which matches the defendant’s is an event of significant probative value, an event of which the jury should almost certainly be informed. Yet the numerical index of the print’s rarity, as measured by the frequency of its random occurrence, may be more misleading than enlightening, and the jury should be informed of that frequency — if at all — only if it is also given a careful explanation that there might well be many other individuals with similar prints. The jury should thus be made to understand that the frequency figure does not in any sense measure the probability of the defendant’s innocence.
84 Harv.L.Rev. at 1355
Professor Tribe’s main point is not that it is necessarily wrong to inform the jury of the underlying statistical evidence but that there is a real danger that the jury will use the evidence as a measure of the probability of the defendant’s guilt or innocence, and that the evidence will thereby undermine the presumption of innocence, erode the values served by the reasonable doubt standard, and dehumanize our system of justice.
It does not follow from either the Carlson case or Professor Tribe’s article that the correct approach is to suppress the evidence entirely, as the trial court did. We believe that the trial court may appropriately limit Dr. Polesky’s testimony so as to omit reference to the degree of probability that defendant is the father of the child and to omit reference to the number of unrelated men one would have to randomly test before one would find another man who could have been the father of the child. On the other hand, Dr. Polesky should be permitted to testify as to the basic theory underlying blood testing and should be permitted to testify that not one of the 15 tests excluded defendant as the father of the complainant’s baby. We believe that his hypothetical opinion should be limited to the following: that the scientific evidence in the form of the test results is consistent with the view that defendant is the father of the baby.

331 N.W.2d at 482-83.

Kim, the third case in the Carlson-Boyd-Kim trilogy, was a pretrial state’s appeal of an order in a rape case suppressing expert testimony that 96.4% of males, but not defendant, could be excluded on basis of combination of blood factors found on the victim’s bed sheet, despite the state’s contention that use of an exclusion rather than inclusion percentage reduced the danger that the jury would misinterpret and misuse the statistical evidence. We said:

The danger we recognized in Boyd is that statistics on the frequency with which certain blood combinations occur in a population will be understood by the jury to be a quantification of the likelihood that the defendant, who shares that unique combination of blood characteristics, is guilty. This danger exists as much in an inclusion as in an exclusion figure because, as the trial court noted, faced with an exclusion percentage, a jury will naturally convert it into an inclusion percentage. * * *
* * * The state argues that the effect of Boyd is to exclude from the factfinding process reliable scientific evidence with great probative evidentiary value. The probative value of such evidence is, however, not of controlling significance in the analysis we adopted in Boyd. Under the Minnesota Rules of Evidence, relevant evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice. Minn.R.Evid. 403. In Boyd, we clearly determined that the danger of population frequency statistics * * * unfairly prejudicing a defendant due to its “potentially exaggerated impact on the trier of fact” outweighed any probative value * * *.
As in Boyd, the expert called by the state in this case should not be permitted to express an opinion as to the probability that the semen is Kim’s and should not be permitted to get around this by expressing the opinion in terms of the percentage of men in the general population with the same frequency of combinations of blood types. The expert should be permitted to testify, however, as to the basic theory underlying blood testing, to testify that not one of the individual tests excluded Kim as a source of the semen and to give the percentage of people in the general population with each of the individual blood types, and to express an opinion that scientific evidence is consistent with Kim having been the source of the semen.

398 N.W.2d at 548-49.

The advocates for the admission in Carlson-Boyd-Kim of the probability figure obtained by using the multiplication rule to combine the individual frequencies of the various blood types were certain of the correctness of the use of the multiplication or product rule of statistical theory. However, the state’s own expert in this case, Professor Hartl, said in an affidavit dated December 8, 1993:

[I]t is my belief that the Kim rule was correct at a time when genetic typing could be performed only with blood groups and other types of genetic systems that are not highly polymorphic; the effect of the Kim rule is to prevent a series of genetic matches at different loci, none individually uncommon, from being combined by a long chain of multiplication of probabilities to yield a small, and unjustified, match probability for the whole set of genes.

As we said, heretofore, in answering the question as to the form the presentation of expert opinion testimony on the issue of identity based on DNA identification techniques should take in a criminal case, we have followed the approach of the Carlson-Boyd-Kim trilogy. See Schwartz, 447 N.W.2d at 428; Nielsen, 467 N.W.2d at 620; Johnson, 498 N.W.2d at 13-15; State v. Alt, 505 N.W.2d 72, 72 (Minn.1993).

As the defendant’s counsel points out, if this court had not ruled as it did in the Cavlson-Boyd-Kim cases, we would now be facing the task of reviewing or re-reviewing convictions based on the admission of such evidence. Similarly, if this court had admitted everything the forensic proponents of DNA technology had advocated, we might be in the same position now in the DNA context that we would have been in if we had admitted the statistical probability evidence based on blood testing in Cavlson-Boyd-Kim.

Since it may be pointless to expect ever to reach a consensus on how to estimate, with any degree of precision, the probability of a random match and that, given the great difficulty in educating the jury as to precisely what that figure means and does not mean, it might make sense to simply try to arrive at a fair way of explaining the significance of the match in a verbal, qualitative, non-quantitative, nonstatistical way.

Notwithstanding this and notwithstanding the fact that the intense debate continues concerning the most reliable, accurate way of estimating random match probability and the proper role of statistical evidence in criminal trials, we now conclude, based on all the circumstances, including the very conservative nature of the probability figures obtained using the NRC’s approach, that a DNA exception to the rule against admission of quantitative, statistical probability evidence in criminal prosecutions to prove identity is justified. Accordingly, any properly qualified prosecution or defense expert may, if evidentiary foundation is sufficient, give an opinion as to random match probability using the NRC’s approach to computing that statistic.

We also conclude that, in an appropriate case, where there is an underlying statistical foundation for such an opinion, a properly qualified expert should be allowed to say more than that the DNA test results merely are consistent with the defendant’s being the source of the physical evidence left behind by the assailant. This modification of Kim does not stem from a belief that this court was wrong in limiting the expert to the use of the “consistent with” language in the Carlson-Boyd-Kim trilogy. Indeed, the state’s own expert says that we were right. Rather, it stems from the belief that the reason for such a limitation, while present in those cases, is not always present in the DNA context and is not present in this case. The underlying probability figure in Carlson was 1 in 4,500; the figure in Boyd was 1 in 1,121; the corresponding figure in Kim was that 96.4% of men could be excluded but not defendant. In our opinion, given the underlying statistical evidence, the only fair way of verbally presenting this evidence in a qualitative rather than quantitative way was to say that the microscopic analysis evidence was “consistent with” the foreign hair being defendant’s (Carlson), that the blood test evidence was “consistent with” defendant’s being the father (Boyd), and that the blood test evidence was “consistent with” defendant’s being the source of the semen (Kim).

In the fingerprint context, some courts apparently allow experts to testify in conclusive terms, as by saying, “In my opinion the print on the ... could not have been made by anyone other than the accused,” or to state their opinions as fact, as by saying, “[M]y comparison and identification established as a fact that the latent print and the actual print were made by the same person.” James R. Richardson, Modem Scientific Evidence § 18.8, at 541 (1974). Our unanimous 9-0 opinion in State v. Spencer, 298 Minn. 456, 216 N.W.2d 131 (1974) (neutron activation expert should not have been allowed to testify that tests showed conclusively that defendant had fired a gun and that there was no unreliability about neutron activation analysis), which was decided before Carlson-Boyd-Kim, supports precluding even a fingerprint expert from testifying in conclusive terms. As a matter of fact, it appears that other courts have refused to permit the opinion to be so stated:

Some courts have permitted fingerprint experts to testify factually while some have refused to do so. Certainly, expert opinion in various fields necessarily varies in its reliability and the intensity with which it is held and expressed. An opinion may be ill-founded and have no probative value; an opinion may be based upon reasonable certainty and, hence, be admissible for weighing of its probative value * * *.

Richardson, supra, at 542 (footnote omitted).

We have concluded that the DNA expert should be allowed to express the opinion that there is a “match” between the defendant’s DNA profile and that left by the assailant at the scene or on the victim. The strength of the expert’s opinion is something the jury should be told; it will depend in part on the degree of the expert’s confidence in the opinion and in part on the underlying statistical foundation for the opinion. We also agree with Professor Kreiling that the expert should be allowed to phrase the opinion this way: that given a reliable multi-locus match, the probability that the match is random or coincidental is extremely low. Kreiling, supra, at 479.

The expert should not, of course, be allowed to say that a particular profile is unique. Thompson, supra, at 87. Nor should the expert be allowed to say that defendant is the source to the exclusion of all others or to express an opinion as to the strength of the evidence. But should a properly qualified expert, assuming adequate foundation, be allowed to express an opinion that, to a reasonable scientific certainty, the defendant is (or is not) the source? We believe so. In reaching this conclusion, we merely are saying, as we intended all along, that the admissibility in a criminal trial of qualitative expert opinion testimony on DNA identification techniques be governed by the same basic rules of admissibility that historically have applied to qualitative expert opinion testimony based on other scientific identification techniques. See, e.g., State v. Rean, 353 N.W.2d 562, 564 (Minn.1984) (where there was expert opinion testimony that it was “highly probable” that shoe prints found at scene were made by defendant’s shoes).

We believe that allowing this sort of verbal, qualitative, non-statistical presentation of the underlying statistical evidence will lead to more agreement among reputable experts at trials and may decrease the likelihood of there being a battle of experts (over the reliability of the random match probability figure), with one expert cancelling out or discrediting the other.

Needless to say, any rule of evidence “cuts both ways.” The defendant in a criminal ease has the same right as the state to present both quantitative and/or qualitative DNA evidence under the rules we today articulate.

Moreover, the trial court of necessity retains its historic power under Minn.R.Evid. 403 and of course has the responsibility of crafting appropriate cautionary instructions. Prosecutors and trial courts are cautioned that we will not hesitate to award a new trial to a defendant if our review of the trial record reveals that quantitative or qualitative DNA identification evidence was presented in a misleading or improper way.

Reversed in part and remanded for trial.

GARDEBRING, Justice

(concurring specially).

I concur in the result reached by the majority opinion, that both expert opinion evidence as to the strength of the match between the samples, and the random match probability statistics which underlie the opinion, may be admitted. I write separately, however, because I am less reluctant than the majority to see the evidence admitted. The techniques for the formulation of DNA evidence, including the underlying statistics as to probability of a match, have been refined extensively over the last decade, and are now quite reliable. In 1994 the work of trial courts, and defense counsel, in appraising the foundation for such expert testimony, in evaluating the quality of laboratory analy-ses underlying the expert opinion and in explaining the use of such evidence to a jury, appears to be no more difficult with regard to this evidence than it would be as to any other type of complex technical material, which is often in evidence in both civil and criminal matters. DNA analysis provides a strong tool for law enforcement in identifying alleged perpetrators of criminal activity and bringing them to trial — both the expert opinion and the underlying statistical bases should be readily used.

However, because it is such a strong tool, its use should be structured in such a way as to give criminal defendants a meaningful opportunity to respond, and I am concerned that the majority opinion gives short shrift to that need. First, trial courts in cases involving DNA opinion and statistical evidence must assure that the provisions of Minn. R.Crim.P. 9.01 are stringently enforced so that defense counsel may have notice, as early as possible in the preparation of the case, that the prosecution will attempt to use this powerful tool. Secondly, law enforcement personnel are reminded that division and preservation of samples, so that defense counsel may obtain independent analysis, is critical in these cases. Third, the trial court must be sensitive to the need for expert assistance in these matters and must assure public funding for this expert assistance where the defendant is indigent.

Finally, I wish to note my concern with the majority’s treatment of the issue of jury instructions. It may be the ordinary course for the development of jury instructions to occur on a case-by-case basis, as trial courts struggle with the issue and experiment with alternative formulations which are then subject to review by appellate courts. However, here, because of the powerful nature of the evidence, and because of the potential for misunderstanding by the jury, I conclude that some direction as to an acceptable jury instruction is needed now. Therefore, I join in the portion of Justice Page’s special concurrence which identifies the matters to be covered by an appropriate cautionary instruction.

PAGE, Justice

(concurring specially).

Today the court concludes that DNA random match probability statistics may be admitted in criminal prosecutions. I concur in that result. I am uncomfortable, however, with the court’s analysis. I write separately to address the court’s specific concern as set out in Kim and to express my frustration with the climate in which our decision is made. The real issue before the court, despite all of the hysteria surrounding the admission of DNA random match probability statistics, is simple. The reason for excluding DNA random match probability statistics was clearly stated in Kim, which analyzed the problem under Minn.R.Evid. 403: “[t]he danger we recognized in Boyd is that statistics on the frequency with which certain blood type combinations occur in a population will be understood by the jury to be a quantification of the likelihood that the defendant, who shares that unique combination of blood characteristics, is guilty.” State v. Joon Kyu Kim, 398 N.W.2d 544, 548 (Minn.1987).

If the jury can be prevented from misusing DNA random match probability statistics, then such evidence should, unless barred by another Rule of Evidence, be admitted. Kim, and the related cases discussed in the opinion, did not carve out a special exception to the Rules of Evidence for statistical evidence. Rather, those cases wrestled with the difficult matter of considering whether the probative value of certain evidence was substantially outweighed by the evidence’s capacity to mislead the jury. DNA random match probability statistics should be admissible provided the information is relevant, provided its probative value is not substantially outweighed by its capacity to mislead thé jury, and provided no other Rule of Evidence bars its admission. The Rules also envision that cross.-examination of expert witnesses and challenges to the foundation supporting the evidence will assist the jury in deciding what weight the evidence should be given.

Trial courts control the information presented to the jury by applying the Rules of Evidence. They also have the tool of the jury instruction to ensure, as best as humanly possible, that the jury uses the evidence presented in the correct manner. With the complex issues posed by DNA random match probability statistics, this court should provide guidance to trial judges in drafting jury instructions, not simply forecast that such instructions will develop on a ease-by-case basis.

At a minimum, the jury should be provided with cautionary instructions that clarify what random match probability statistics prove and what further conclusions only can be reached by inference. Jurors must, understand the very precise and limited meaning of DNA statistics. They also must understand which conclusions represent inferences that go beyond the statistics themselves. At the very least, jurors should know:

(1) A given DNA profile may be shared by two or more people;
(2) The random match probability statistic is not the equivalent of a statistic that tells the jury the likelihood of whether the defendant committed the crime;
(3) The random match probability statistic is the likelihood that a random person in the population would match the characteristics that were found in the crime scene evidence and also in defendant’s DNA;
(4) Where the known DNA sample from the defendant matches the unknown sample obtained from the crime scene, it does not necessarily mean the defendant is the source of the sample found at the crime scene; and
(5) That jurors alone have the final responsibility to decide the weight to be given to DNA random match probability statistics.

My final comments concern the clamor surrounding the issue of admitting DNA statistical evidence. In Bloom, the key issue to be decided by the court is whether the concerns expressed in Kim could be adequately addressed. Unfortunately, the parties chose not to respond directly to that issue — how to avoid misleading the jury. The parties instead focussed on the reliability of DNA evidence; that is, whether the evidence was too strong to be inadmissible or too weak to be admissible. While such concerns are significant, the single-minded focus on the issue of reliability alone did not assist the court in responding to the central issue of this case.

This court relies heavily on the information parties present to us in their briefs and oral arguments. When it is apparent that our decision will have repercussions extending far beyond the fate of this particular defendant, counsel best serve the administration of justice when they argue how the law, the facts, and sound public policy support their position. Exaggeration, hyperbole, and misinformation disserve the court. This court cannot play to the media’s penchant for drama or the legislature’s perceived need for immediate action. We have the responsibility to apply the law to facts established as firmly as possible, on the basis of dispassionate reason.

At oral argument, we were told that only Minnesota and one other state prohibited the introduction of population genetics statistics. When asked for case citations, counsel for the state referred the court to a footnote in a law review article, to recent Illinois and New York eases, and later provided a list of citations to 44 cases from other jurisdictions. These references were not helpful. It would have been preferable to have had some analysis of the reasoning of other courts on the concerns we raised in Kim.

Review of several of the cases on the list suggests the claim advanced at oral argument as to the admission of DNA random match probability statistics by other courts was misleading. In State v. Bible, 175 Ariz. 549, 858 P.2d 1152 (1993), the court stated: “We simply hold that statistical evidence of the random match probabilities was inadmissible and, thus, should not have been admitted.” Id. 858 P.2d at 1190. In Commonwealth v. Lanigan, 413 Mass. 154, 596 N.E.2d 311 (1992), the appellate court affirmed the trial court’s decision to exclude DNA random match probability evidence because the judge found the scientific community was divided on the validity of the comparison databases. Id. 596 N.E.2d at 314-16. The court in Lanigan followed Commonwealth v. Curnin, 409 Mass. 218, 565 N.E.2d 440 (1991). Cumin held it was prejudicial error to admit random match probability statistical evidence. Id. 565 N.E.2d at 445. Perhaps a reading of all the cases on the list would prove the list as a whole was not substantially misleading, ignoring that many cases were from intermediate and not final appellate courts. More helpful to this court than a simplistic effort to “count noses” from opinions which deal with different parts of a very broad set of problems would have been careful analysis of these cases on the precise issue before us in Bloom.

The cases referenced at oral argument concerned the issue of the reliability of DNA statistical evidence. The Illinois case, People v. Watson, 257 Ill.App.3d 915, 196 Ill.Dec. 89, 629 N.E.2d 634 (1994), is from an intermediate court and so does not represent Illinois’ final position. The New York case was People v. Wesley, 83 N.Y.2d 417, 611 N.Y.S.2d 97, 633 N.E.2d 451 (1994). The use made of DNA evidence in Wesley was very different than in Bloom: DNA profiling was used to match blood found on the defendant’s clothing with the victim’s blood, not, as in this ease, to compare a specimen taken from the victim with a database containing thousands of DNA profiles. In short, Wesley, in terms of its factual setting, its focus on reliability, and its analysis, is not at all similar to Bloom.

The court’s decision today does not close the book on the issues involved in the admissibility of DNA evidence. At most, it represents but one small chapter, one which comes quite early in the story.

TOMLJANOVICH, Justice

(concurring specially).

I join in the special concurrence of Justice Page.

COYNE, Justice

(dissenting).

I dissent. I agree, of course, as I did five years ago when we decided in State v. Schwartz, 447 N.W.2d 422 (Minn.1989), that when a proper foundation has been laid—that is, when there has been a showing that the tests were performed in accordance with appropriate laboratory standards and controls — DNA test results are admissible into evidence. At that time we hedged DNA testing about with the same procedural safeguards applicable to other kinds of scientific evidence: to insure a fair trial, the test data and methodology must be available for independent review by or on behalf of the opposing party, and the admissibility of statistical probability evidence should be limited pursuant to Rule 403 of the Minnesota Rules of Evidence, which permits the exclusion of relevant evidence if its probative value is substantially outweighed by the danger of unfair prejudice. See State v. Kim, 398 N.W.2d 544, 548 (Minn.1987).

Today the majority has bulldozed that hedge into oblivion, ostensibly in the interest of “scientific proof,” with only a backward glance at the reason for excluding statistical probability evidence. Statistical probabilities are certainly useful tools for indicating the direction and utility of further scientific research and for supporting certain conclusions with respect to the validity and use of the results of the research. Statistics have, however, been known to lie — either inadvertently or purposefully. The debate surrounding the National Research Council’s recommendation for the development of a conservative “interim ceiling method” and the Council’s acknowledgment that the methods of calculating the probability of a random match, current at the time its 1992 report was issued, rest on inadequate data and unjustified assumptions about population substructure, both bear witness to the fallibility of statistical evidence. More germane to the present case, perhaps, is the wide divergence in the statistical probabilities proffered by the state’s two experts, both professing to use the “interim ceiling method:” The BCA’s forensic technician is prepared to testify to a 1 in 93,700 chance that a randomly selected person’s DNA would match at the five loci where he matched the defendant’s record to the specimen found at the crime scene. The imported expert, however, is prepared to testify to a 1 in 634,687 chance of a random match.

The accuracy of a statistical probability may be of little moment to the scientific community because although discovery of the falsity of an assumption underlying a statistical probability may destroy the value of the statistic, that discovery may confirm the validity of the basic research. If, however, an erroneous statistical probability plays any significant role in the conviction of an innocent person, the error has not only destroyed the life of the innocent person but has in some sense dehumanized the community. The point is illustrated by the proof of mathematical probability received as evidence in the infamous Dreyfus case in 1899.

In the light of the potential for invalidity of the assumptions about the frequency of a particular pattern of DNA at a given locus, about population substructure, and about statistical independence, I am not persuaded that there is any more justification for admitting statistical probabilities with respect to DNA than there was for admitting probabilities in State v. Carlson, 267 N.W.2d 170 (Minn.1978), or in any of its progeny. Cf., Friedman v. Commissioner of Public Safety, 473 N.W.2d 828, 838, 843-45 (Minn.1991) (Coyne, J., dissenting) (explaining my approach to overruling established precedent; dissent joined by Keith, C.J.) If the underlying assumption is wrong, the statistics are worthless. Conversely, the price of error is too high.

More to the point, perhaps, than the potential for error in these statistics is their potential for misuse. The state’s imported expert witness is prepared, as I have already noted, to testify that there is a 1 in 634, 687 chance of a random match at the five loci in question. That figure is, in a sense, fictitious; the witness concedes that he used the “interim ceiling approach” with its built-in adjustments. Statistical probabilities are, of course, only probabilities — estimates, not certainties. As the witness undoubtedly recognizes, however, the mere recitation of the number 634,687 conveys an aura of mathematical precision, lending the probability a credibility it may not deserve and a weight to which it has no logical claim.

A quarter-of-a-century ago the California Supreme Court observed that “[mjathemat-ics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not [be allowed to] cast a spell over him.” People v. Collins, 68 Cal.2d 319, 66 Cal.Rptr. 497, 438 P.2d 33, 33 (1968) (en banc). Surely, the almost universal acceptance of accuracy and precision in mathematical calculations has not diminished in the intervening years.

More inimical to our traditional system of legal proof in criminal trials than undeserved credibility is the danger that the fact finder will understand the statistic represents something which it does not — namely, that the probability refers to the odds that someone else than the defendant is the source of the specimen found at the scene of the crime. That mistake has so often found its way into the rhetoric of public figures and in erroneous reports in the public press that it may be impossible to erase it from the mind of the fact finder. Even the state’s expert fell into that trap on cross-examination.

Moreover, it seems to me that the preoccupation with statistical evidence is very likely to divert attention away from those aspects of DNA evidence which are deserving of closer examination. Are the test results reliable? What is the laboratory’s “false positive match rate”? Does the laboratory which performed the tests observe rigorous, scientific standards and quality control? Did the technicians follow laboratory protocol in the tests in question? Does the laboratory have an objective and quantitative procedure for identifying patterns, and a clearly defined procedure for declaring a match, identifying potential artifacts and designing internal controls to determine the presence of the artifact in a particular test? In short, there are inherent limits to any particular technique, test results can be skewed by a medium which does not meet quality controls or by defective equipment, and there is always the possibility of human error. If the match reported in the present case is erroneous at any one of the five loci, there is no match at all and the statistical probabilities of a random match have no relevance whatever.

Despite my conviction that the admission of statistical probabilities is more likely to be misleading than helpful and that it introduces unfairness into a criminal trial, I do believe that DNA typing has now demonstrated sufficient reliability and particularity to justify some modification of the rule set out in the Kim case, supra. It seems to me that it is more accurate to inform the jury that matches like those present in this case are “rare” or even “extremely rare” than to say only that the test is “consistent with” defendant being the source of the specimen found at the scene of the crime. In keeping with expert testimony in other contexts, I also consider admissible an expression, given an appropriate foundation for the opinion, that to a reasonable degree of scientific certainty the defendant is the source of the specimen. That information places the jury in a suitable position to assess the DNA evidence and protect the right of the defendant to a fair trial while at the same time avoiding the pitfalls attendant upon the illusion of mathematical precision.

This court has heretofore adhered to the principle that conviction of the defendant in a criminal trial depends on the jury’s determination that, based on all of the evidence before it, the state has proved the defendant’s guilt beyond a reasonable doubt and that a criminal trial should not be resolved by a battle of experts. That a civil case should turn on the opinion of competing experts is considered by some as cause for alarm. That a criminal trial should be determined on the basis of probability estimates ought to give all of us pause.

That mine is the lone dissenting voice in this matter does not shake my conviction that the day will come when this court regrets today’s decision. 
      
      . These cases are: the instant case, State v. Bloom, 516 N.W.2d 159; State v. Perez, 516 N.W.2d 175; filed herewith; State v. Bauer, 516 N.W.2d 174, also filed herewith.
     
      
      . The appeal in this case is an accelerated appeal by the state of a pretrial suppression order in a rape prosecution. The appeals in Perez and Bauer are post-trial appeals by defendants from judgments of conviction.
      The alleged facts in this case are as follows: Shortly after 1:00 a.m. on November 23, 1992, J.L.P., a 34-year-old woman, was entering her home in Brooklyn Park when she was grabbed from behind by a Caucasian man. The man, whom she did not see well enough to identify, forced her into her car, pulling a stocking cap over her face. He drove her to a different location, ordered her into the back seat, and told her if she did not comply with his demands he would penetrate her vagina with a screwdriver. He forced her to submit to fellatio, digital penetration and ordinary sexual penetration. He also bit the victim on her breasts. After assaulting her, he drove her home and dropped her off, then abandoned her car nearby.
      After preserving semen samples taken from the victim in the sexual assault examination and other semen samples found in the car, the BCA, prepared a DNA profile of the samples. This consisted of six separate probes and resulting autorads for comparison with autorads made from probes of known DNA.
      James Liberty, who does forensic work at the BCA and has attended an FBI course on forensic aspects of DNA technology, testified that using information from two of the six probes to make a computer search of the BCA’s sex-offender DNA database, he came up with five potential suspects, including defendant, whose DNA matched at those two loci. Comparing the probe data of the five potential suspects found in this manner, he determined that one of them, defendant, "stood out.” Then, by comparing the database pattern at all five loci available in defendant's prior database profile he determined that there was a match with the pattern at all five loci on the autorads made from the assailant's semen.
      Liberty then did another complete DNA test on both the assailant's semen and on a new sample of defendant’s blood, taken after his arrest, as well as on blood from the victim's boyfriend and from another individual, and he produced new autorads. The victim's boyfriend and the other individual were excluded as possible sources. The defendant's DNA profile matched the crime scene sample at all nine loci tested.
      After using five loci and finding a match at each, Liberty made some calculations and concluded that there was a 1 in 93,700 chance that a randomly selected person would match at all five points.
      Professor Daniel Hard, a Professor of Biology at Harvard and an earlier critic of some of the statistical computations that forensic scientists were making based on FBI databases, testified (by telephone) for the state at the suppression hearing that, using the "interim ceiling method” recommended by the National Research Council, there was a 1 in 634,687 chance of a random match across the five loci. He testified that Liberty had obtained the less-impressive 1 in 93,700 figure by making some "adjustments” that were not needed because the interim ceiling approach, which Liberty too had used, had those adjustments built into it. Dr. Hartl, if permitted, would further testify at trial that in fact there was a nine-loci match and that in his opinion the nine-loci match constituted "overwhelming evidence that, to a reasonable degree of scientific certainty, the DNA from the victim’s vaginal swab came from [defendant], to the exclusion of all others.”
      The trial court, relying on the Carlson-Boyd-Kim trilogy, discussed infra, and subsequent cases applying the Kim rule in the DNA context, ruled (1) that the jury could be told (a) that defendant's DNA was consistent with crime scene samples on each of the nine bands tested, (b) the frequency of each individual band and (c) nonstatistical opinion testimony that defendant's DNA profile is consistent with that of the assailant, but (2) the jury could not be told (a) that the frequency of the profile in the population based on five tests is 1 in 634,687 (or, for that matter, 1 in 93,700) or (b) that the opinion of Dr. Hard is as just quoted. The court ruled further that the state would be permitted to use two of defendant's prior similar offenses as Spreigl evidence.
     
      
      . Harsh criticism of the FBI's alleged role in suppressing negative DNA research, in refusing scrutiny of its databases, in intimidating certain scientists, and in attempting to undermine the NRC Committee’s independence appears in Thompson, as well as in Peter J. Neufeld, Have You No Sense of Decency, 84 J.Crim.L. & Criminology 189 (1993). Thompson states that at one point the FBI, in response to an NRC Prospectus that suggested the new committee would also "[a]ssess and describe the degree of certainty of DNA evidence in ways useful to the courts,” threatened to withhold funding of the new study unless the NRC limited the scope of its inquiry to procedures for estimating frequency of DNA profiles in a reference population. Thompson, supra, at 82 n. 280.
     
      
      . The most interesting recent legal analysis bearing on this is that of Professor Kenneth R. Kreil-ing of the University of Vermont Law School in a 39-page critical review of the NRC Report. See Kreiling, DNA Technology in Forensic Science, supra. Kreiling notes that the Report, in the chapter dealing with "Statistical Basis for Interpretation” (Chapter 3), begins by saying, "To say that two patterns match, without, providing any scientifically valid estimate (or, at least, an upper bound) of the frequency with which such matches occur by chance, is meaningless.” Id. at 464. But Kreiling notes that "the chapter then goes on to explain the inherent difficulty of calculating valid frequency estimates for highly polymorphic DNA loci,” and adds, "[t]he commitment to providing the estimate, in light of the inherent difficulty, haunts the Committee's quest to reach an acceptable solution to the controversy." Id. And he notes later that the Report inconsistently suggests at one point that courts might decide not to permit the expert to characterize the probability of a match in mathematical terms. Id. at 477; NRC Report § 6.5, at 6-15. After carefully discussing the scientific controversy that, notwithstanding the NRC Report, continues as to how to best estimate the probability of a random match, Kreiling states:
      David McCord and others have documented the earlier reluctance of commentators and courts to admit unreliable probability evidence. The Committee, clearly wary of the problems associated with such evidence, jumped on the bandwagon to provide the optimal probability figure in DNA cases and made a recommendation which is unlikely to be widely adopted. Perhaps a more prudent recommendation would have been to call for un-controvertible data or verbal formulation of the improbability of a random match pending a real, rather than a forced, consensus on how a reliable probability figure could be provided. The probability of a random match is extremely remote given a reliable multilocus match. This fact easily can be conveyed, and is in fact typically conveyed, verbally to the jury in the context of explaining the genetic basis of the technique. Why have the proponents of DNA evidence, the U.S. courts and the Committee, insisted on providing a possibly unreliable probability figure, one which will only cause controversy and diminish jury comprehension of the technique, to convey the obvious? Absent a reliable figure, the additional probative value provided by the numerical guesstimates is negligible, if not negative, and is substantially outweighed by the dangers of confusing the issues, misleading the jury, and wasting time.
      The continuing conflict over the appropriate statistical figure will unfortunately obscure other important issues about DNA testing. Attorneys and the jury, if they continue to wage debate over the appropriate probability guesstimate, will tend to underemphasize other issues which the Committee deemed important, and which the jury should consider without unnecessary statistical "noise.” Human error in applying the complex multistep technology may be overlooked. Subjective aspects of interpreting the images [on the autorads] may not be challenged. The question of error rates and false positives may not be raised or, if raised, lost in the conflict over probabilities. The danger of random match probabilities be-, ing erroneously converted by the trier into a probability that the defendant is the source of the evidence continues and may be exacerbated by the lower ceiling principle guesstimates. The question of the appropriate reference population for the estimate has been and will probably continue to be obscured by debate. Perhaps most significant, the lengthy battle over probability estimates may obscure the fact that the question of guilt is a function of all the evidence in the case.
      
        Kreiling, supra, at 479-80 (footnotes omitted).
     
      
      .There remain (a) the “gender bias” argument advanced by the state and (b) the issue of whether to admit evidence that defendant's profile was the only one found in the BCA database that matched the DNA profile of the unknown suspect.
      (a) In its petition for rehearing in the trial court, the state for the first time claimed that exclusion of the random match probability constitutes "gender bias" because in a large majority of the cases in which DNA evidence is used the victims are women. The trial court did not address the issue. The state raised the issue in its brief, arguing emotionally, "The time has come to stop settling the rights of defendants on the backs of female victims of sexual violence.” However, we note that the state’s attorney did not argue the issue in oral argument. Suffice it to say, our decisions governing the presentation of expert opinion testimony based on DNA identification techniques are equally applicable in all criminal cases regardless of the gender of the victims or the defendants, and we have no difficulty in rejecting this argument.
      (b) The trial court's order permits the state to present evidence that defendant’s profile was the only one in the BCA database that matched the DNA of the unknown semen. While there may be merit in informing the jury that a search of a database containing defendant's DNA and the DNA of a number of other people led to the discovery of a preliminary "match” and to the state's focusing on defendant as a suspect, we see no need to inform the jury of the fact that the database is the BCA’s database of sex offenders.
     
      
      . In exercising its discretion under Rule 403, the trial court should assure itself that the defendant has had adequate notice of the state's intended use of the evidence; that the state has taken all reasonable steps to preserve the bodily samples so that a defense expert may, if the defense so chooses, subject the evidence to independent analysis; and that any indigent defendant has reasonable access to expert support at public expense.
     
      
      . The content of cautionary instructions must develop on a case-by-case basis.
     
      
      . I also have serious concerns with respect to the underlying science and technology used to develop the DNA random match probability statistics. These concerns include the fact that a given DNA profile can be shared by two or more people; the potential for human error; the fact that we can, with some degree of mathematical certainty, expect a certain number of false positives for each 100 samples tested; the lack of uniform minimum quality control standards and procedures for laboratories conducting DNA tests; and, as noted by counsel for the state, if a sample of my blood were taken and tested 100 times on the same day, the result would not be the same every time. Having concluded some time ago that DNA evidence may be admissible subject to the proper foundation, most of these concerns may presumably be addressed on a case-by-case basis through challenges to the foundation of the DNA evidence. With respect to quality control standards and procedures for testing laboratories, I believe that, at a minimum, laboratories conducting DNA testing should be required to comply with the standards and procedures required of laboratories conducting drug and alcohol testing under Minn.Stat. §§ 181.950 — .957 (1992).
     
      
      . By ''inference,” is meant "the act of passing from one or more propositions, statements, or judgments considered as true to another the truth of which is believed to follow from that of the former.” Webster’s 3rd New International Dictionary Unabridged 1158 (1993).
     
      
      . There are law review articles suggesting the contrary. See e.g., Christopher G. Shank, DNA Evidence in Criminal Trials: Modifying the Law's Approach to Protect the Accused from Prejudicial Genetic Evidence, 34 Ariz.L.Rev. 829, 854-56 (1992); William C. Thompson, Evaluating the Admissibility of New Genetic Identification Tests: Lessons from the "DNA War," 84 J.Crim.L. & Criminology 22, 23, n. 5, 81 (1993) (noting nine appellate and ten trial court decisions holding DNA evidence inadmissible and citing FBI Director William Sessions' observation that "since the release of the NRC Report, eleven of thirty appellate decisions on the admissibility of DNA evidence have ruled it inadmissible”). The sources do not specify whether DNA evidence was found to be generally inadmissible or inadmissible under the particular facts of the case.
     
      
      .The list was received eleven days after oral argument and four days before this opinion was filed.
     
      
      . As Professor Laurence H. Tribe remarks in Trial by Mathematics: Precision and Ritual in the Legal Process, 84 Harv.L.Rev. 1329, 1333 (1971), "the 'mathematics’ on which [the probabilities that an incriminating document was used to convey coded information] were based was in fact utter nonsense.”
     
      
      . An artifact is a variation in the appearance of the photo-image caused by limitations in the technique or its improper application.
     