
    933 P.2d 1187
    STATE of Arizona, Appellee, v. Steven Henry HUMMERT, Appellant.
    No. CR-95-0100-PR.
    Supreme Court of Arizona, En Banc.
    March 11, 1997.
    Reconsideration Denied April 29, 1997.
    
      Grant Woods, Arizona Attorney General by Paul J. McMurdie and Randall M. Howe, Phoenix, for the State of Arizona.
    Alex D. González, Mesa, for Steven Henry Hummert.
   OPINION

FELDMAN, Justice.

Steven Henry Hummert (Defendant) appealed his convictions for kidnaping, sexual assault, sexual abuse, and aggravated assault. Defendant claimed the trial judge erred in admitting evidence of DNA testing. Following State v. Bible, 175 Ariz. 549, 858 P.2d 1152 (1993), cert. denied, 511 U.S. 1046, 114 S.Ct. 1578, 128 L.Ed.2d 221 (1994), the court of appeals held that experts can only testify a DNA match means the defendant cannot be excluded as the donor of the sample. State v. Hummert, 183 Ariz. 484, 905 P.2d 493 (App.1995). Furthermore, the court of appeals found that the experts’ testimony about their personal experience of random matches at three loci had the effect of communicating to the jury that the DNA conclusively came from Defendant. This, the court of appeals held, was prejudicial error. Id. Therefore, the case was reversed and remanded. We accepted review pursuant to Rule 31.19 of the Arizona Rules of Criminal Procedure. We have jurisdiction under Arizona Constitution, art. VI, § 5(3).

FACTS AND PROCEDURAL HISTORY

In the early morning hours of July 16, 1989, a nineteen-year-old Tempe woman and a friend were driving home from a dance club when they noticed a red Honda CRX with gray out-of-state license plates and an emblem shaped like Texas on the rear. The Honda was traveling in a different direction and turned at an intersection. A little while later they saw the same car turning in yet a different direction at another intersection.

The woman dropped off her friend and went on to her boyfriend’s home, but he was not there. Again she thought she saw the red Honda. When she arrived home at approximately 3:30 a.m., a man surprised her as she was leaving her car and forced her into a neighbor’s yard at gunpoint. As he did so, she saw the same red Honda CRX and was able to remember part of the license plate number. The man then raped her. The attacker attempted to strangle the victim, and in the struggle she bit him on his forearm. During the assault, he hit her around the face and head, perhaps with the butt of his gun or against a brick planter, causing severe lacerations and loss of consciousness. When she woke up, the red Honda was gone.

The victim described the car and license to the police and family members at the hospital. Propitiously, a cousin who had visited her at the hospital stopped at a nearby Mc-Donalds, where he saw a red Honda CRX with Texas plates and a Texas-shaped emblem on the back. Defendant, who owned the car, worked at the McDonalds as a manager. When questioned by the police, Defendant claimed to have been at a party with people from work at the time of the assault. The co-workers later told police Defendant had asked them to say he left the party at 4:00 a.m. when he actually left at approximately 2:00 a.m. Defendant also had a wound on his arm that was consistent with a bite, and a pubic hair from the crime scene was consistent with his hair. Although the victim picked two other photographs from a pretrial photographic line-up, she identified Defendant as her assailant at trial.

The FBI performed DNA tests using the Restricted Fragment Length Polymorphism (RFLP) method and found that DNA extracted from semen on the victim’s underwear matched Defendant’s DNA at four loci, although one match was not considered because the victim shared the same allele. At trial, the judge admitted evidence of the match, the criteria for declaring a match, and opinions that Defendant was not excluded by the DNA tests. After a Frye hearing, the judge found that although the process of RFLP DNA profiling had been accepted by the relevant scientific community, the methods for calculating the mathematical probability of a random match were not generally accepted. The statistical probability of a random match expresses this possibility in a mathematical percentage. In Bible, for example, the witness testified, in effect, that the probability the blood on Bible’s shirt came from the victim was in a “conservative” range of 60 million to one. 175 Ariz. at 582, 858 P.2d at 1185. Instead of allowing statistics on the probability of a random match, the trial judge only permitted testimony about the uniqueness of DNA and the expert’s personal experience in never finding random matches under the same circumstances. If a match is random, then the sample could have come from someone other than the person in question.

Defendant was convicted of two counts of sexual assault, kidnaping, two counts of aggravated assault, and sexual abuse, all dangerous felonies. Because Defendant had a prior felony conviction and was on probation, he was sentenced to concurrent terms of twenty-five years to life on all counts.

On appeal Defendant challenged the admissibility of the DNA evidence, among other issues. The question before the court of appeals was whether “testimony regarding the existence of a ‘match’ between questioned and known DNA samples [is] admissible,” given Bible’s holding “that random match probability calculations are inadmissible on Frye grounds.” Hummert, 183 Ariz. at 489, 905 P.2d at 497. The court held that under Bible, experts can only testify that a DNA match means the defendant cannot be excluded as the donor of the sample. Because the expert witnesses testified the DNA matched at three loci, the court said this was tantamount to showing conclusively the samples came from the same person. The court found this was prejudicial error because it overstated the significance of the DNA test results, implicitly conveyed to the jury the forbidden random match statistics, and made it practically impossible for the defense to cross-examine the experts without referring to the inadmissible probability statistics. Id. In its opinion, the court cited several cases from other states holding DNA evidence and the declaration of a match inadmissible in the absence of generally accepted population frequency statistics.

DISCUSSION

A. Evolution of the Arizona rule on DNA evidence

We have considered the admissibility and use of DNA evidence in two cases: Bible and State v. Johnson, 186 Ariz. 329, 922 P.2d 294 (1996). The present case was tried before Bible and the appeal argued and decided after Bible but before Johnson. Both cases describe the science involved in DNA testing in some detail. In the present case we make no attempt to review the scientific process except for what may be necessary to explain our reasoning.

The use of DNA profiling and matching in forensics involves three basic steps. First, through a lengthy process of chemical treatment and “photographing” using radioactive probes and X-ray film, profiles (autorads) are created of DNA evidence samples from the crime scene and samples taken from the victim and the suspects. Second, the profiles are analyzed to determine whether any of the samples match. This is done both by sight and computer analysis, comparing whether the pictures of the DNA segments photographed are the same length. Finally, the significance of the match is articulated, usually by calculating the probability of a random match. Bible, 175 Ariz. at 577, 858 P.2d at 1180.

1. State v. Bible and Cellmark’s use of the product rule

Applying Frye, we reviewed the admissibility of DNA statistical probability evidence calculated with the product rule in Bible. We held that while the RFLP method of declaring a match is admissible, the random match mathematical calculations were inadmissable because the laboratory that had applied the product rule used a flawed database. Id. at 581, 858 P.2d at 1184. The Cellmark laboratory maintained a database of DNA samples that were used to calculate how frequently the genes profiled occurred in the general population. However, this database was flawed because it had not been shown that it was in linkage equilibrium, was broad enough to be statistically valid, or was in Hardy-Weinberg equilibrium. See Johnson, 186 Ariz. at 331-33, 922 P.2d at 296-98. The “application of the product rule [by Cell-mark] and the resulting opinion of the odds against a random match were not derived by applying generally accepted scientific theory” because the database was flawed. Bible, 175 Ariz. at 586, 858 P.2d at 1189. Contrary to the court of appeals’ reading, as a general matter Bible did not absolutely reject the use of statistics calculating the probability of a random match. Arguably, with a database that meets Frye requirements, the product rule may be accepted as effective for calculating the probability of a random match. Id. at 590, 858 P.2d at 1193; see also Johnson, 186 Ariz. at 335, 922 P.2d at 300.

2. The need for statistics

The court of appeals stated:

An autorad match is meaningless without the statistical evidence to validate the match. If the autorad reflects only sites on the DNA that are common to all human beings (monomorphic sites), the evidence obtained cannot be the basis for identifying the defendant. Thus, the expert must also show that the alleles detected by the particular probes used are polymorphic.

Hummert, 183 Ariz. at 484, 905 P.2d at 497. The purpose of the statistical interpretation of the match, however, is not to determine whether the loci measured in the autorad were poly- or mono-morphic. Because 99.9 percent of all human DNA is monomorphic— common to all people — the RFLP test has been developed to look at and measure only those areas that are polymorphic — i.e., known to vary widely from person to person. Statistical comparisons to the database are required to determine how often a particular polymorphic combination occurs in the population. All the sites used in the RFLP technique are by definition polymorphic, making a second test unnecessary.

Related to the court of appeals’ misunderstanding of the necessity of the statistical analysis of the probability of a random match was its application of a statement made by the National Research Council (NRC) in its 1992 report, The Evaluation of Forensic DNA Evidence (1992 Report), claiming that “[t]o say that two patterns match, without providing any scientifically valid estimate ... of the frequency with which such matches might occur by chance, is meaningless.” Id. at 74. Courts, particularly the Washington Supreme Court in State v. Cauthron, 120 Wash.2d 879, 846 P.2d 502 (1993), have interpreted this to mean that numerical statistics are required to express the significance of the match of two DNA profiles. We believe this view to be seriously incorrect. First, it is unclear that the NRC intended to say that only numerical expressions are acceptable in court. Furthermore, in a later report, unavailable at the time of the court of appeals’ opinion, the NRC stated:

Scientifically valid testimony about matching DNA can take many forms. The conceivable alternatives include statements of the posterior probability that the defendant is the source of the evidence DNA, qualitative characterizations of this probability, computations of the likelihood ratio for the hypothesis that the defendant is the source, qualitative statements of this measure of the strength of the evidence, the currently dominant estimates of profile frequencies or random-match probabilities, and unadorned reports of a match. Courts or legislatures must decide which of these alternatives best meet the needs of the criminal justice system.

National Research Council, The Evaluation of Forensic DNA Evidence ES-7 (emphasis omitted) (1996) (pre-publication copy) (1996 Pre-Publication Report).

We interpret this to mean that there is no single or specific scientific method of expressing the significance of a match but, rather, different ways of explaining the significance in a forensic setting. Therefore, once an expert witness, using a method such as RFLP that has been accepted as admissible under Frye, has determined there is a match, then the expert may testify and express his or her opinions in several ways that effectively communicate his or her findings. Id. From the scientist’s standpoint, it is for the courts to decide if the expert may testify on the significance of the match as determined by probability statistics, or draw conclusions, as was done in this case, strictly from personal knowledge and study, if this is the type of information the expert regularly and reasonably relies on. See Ariz.R.Evid. 702 and 703. We did not foreclose this issue in Bible. We held instead that when DNA samples “match, the conclusion is that they may be from the same individual.” We went on to conclude there was no general acceptance in the scientific community for Cell-mark’s random match probability calculations and they were therefore inadmissible. Bible, 175 Ariz. at 590, 858 P.2d at 1193. We reserved and

expressly [did] not decide whether the inadmissibility of the random match probability calculations means that other DNA evidence, such as evidence of a match is inadmissible____
We take a cautious conservative approach. Not knowing what records in other cases will show, what issues those cases will raise, or what new technology will bring, we neither write in stone nor go farther than we must____ We make no final judgment on how far, if at all, the court may go in allowing a party to inform the jury about the declaration of a match and its meaning in any specific case.

Id.

3. State v. Johnson

Three years after Bible, armed with recently expressed scientific opinion, we again addressed the issue. After our opinion in Bible, and many cases like it in other states, the relevant scientific community acknowledged the problems arising from questions about DNA databases. In its 1992 Report, the NRC developed a way to make DNA analysis helpful for forensic use. The modified ceiling method uses a database that ensures the random match probabilities calculated are very conservative and protect a defendant’s rights. See Johnson, 186 Ariz. at 333, 922 P.2d at 298. In Johnson, we held that the modified ceiling method had been generally accepted by the relevant scientific community, meaning DNA probability calculations computed using the modified ceiling method are admissible under Frye. Id.

Subsequent to the Johnson opinion, the NRC updated its 1992 Report, concluding that enough information about gene frequency had been gathered in four years to make the conservative approach of the ceiling principles no longer necessary. See 1996 PrePublication Report, at 5-32. The NRC also concluded that alternative methods, including the product rule with qualifications made to cope with subpopulations, isolated populations, and related individuals, are now statistically viable. Id.

B. Expert opinions and scientific evidence

1. Alternative methods

The experts’ testimony in the present case involved two types of evidence— scientific evidence on the procedures for determining a match between evidentiary DNA and opinion evidence concerning the experts’ experience with random matches. The trial judge properly applied the Frye analysis and determined that evidence of a match is admissible. However, on the basis of the scientific evidence then available, the judge did not allow the experts to testify about the mathematical or statistical probability resulting from the match. Instead, the experts were allowed to offer evidence of their personal opinion. This testimony is governed not by the application of Frye but by Arizona Rules of Evidence 702 and 703. See State v. Roscoe, 145 Ariz. 212, 219, 700 P.2d 1312, 1319 (1984). “Frye-ing" scientific evidence is necessary when application of a scientific technique is “likely to have an enormous effect in resolving completely a matter in controversy.” State ex rel. Collins v. Superior Court, 132 Ariz. 180, 199, 644 P.2d 1266, 1285 (1982), quoting M. Udall & J. Liver-more, Law of Evidence § 102, at 212 (2d ed.1982). However, when the expert gives testimony that “only helps a trier to interpret the evidence ... it will be received on a lesser showing of scientific certainty.” Id. As we stated in Roscoe, “[t]he weight of the evidence did not hinge upon the validity or accuracy of some scientific principle; rather, it hinged on [the expert’s] credibility, the accuracy of his past observation ... the extent of the training ... and the reliability of his interpretations____” Roscoe, 145 Ariz. at 220, 700 P.2d at 1320; McCormick on Evidence § 203, at 871, nn. 27 and 28 (J.W. Strong et al., eds., 4th ed.1992). The experts in this case did not testify to conclusions based on the application of Cellmark’s statistics and database but only to their own experience. Having made the DNA examination according to recognized scientific principles and finding a match at three loci, the experts claimed that because of the unique nature of each person’s DNA, they had never before seen a three-loci match from unrelated individuals. On the basis of their own experience, they believed such a random match would be very uncommon. The trial judge did not err in admitting this evidence of the experts’ own work and experience and the opinions reached on that basis. See Ariz. R.Evid. 702 and 703.

2. Opinion evidence as an “end-run” around Frye

The court of appeals suggested that although couched in terms of their personal experience, the experts’ testimony effectively conveyed to the jury the then-impermissible random match probability statistics. We do not agree. Both witnesses explained why they had found a match both visually and numerically. They explained that the profiles matched over four probes, though one of the probe matches was rejected in the interests of accuracy and that the areas looked at by RFLP analysis are polymorphic and vary between individuals. This testimony fit within the scientific evidence category and was permitted because it met the requirements of Frye.

The prosecutor then turned to the experts’ personal experience, developing their experience with the RFLP analysis and the pertinent literature to support their testimony that they had never personally seen or heard of a random match over three or four loci. However, it was also developed that such a match would be possible between identical twins or even brothers. Defendant chose not to cross-examine the experts on the basis for their opinions, instead focusing on the fact that only a small percentage of DNA differs from person to person, the possibility of laboratory error, bias, and environmental insults to the evidence DNA. As noted, this is the very type of opinion evidence discussed in Roscoe, which is not based on the application of scientific principle but, rather, on the observations and credibility of the witness. Thus, it need only meet the requirements of relevancy and not be substantially more prejudicial than probative. See Ariz.R.Evid. 401 and 403.

3. Application of Rule 703

The court of appeals argued that Rule 703 might be used as a way to “back-door” otherwise unacceptable scientific evidence. Under the present state of our cases, however, because scientific evidence, as opposed to opinion evidence, must first meet the requirements of Rule 702 and Frye, we find this highly unlikely. Moreover, a search of cases within Arizona shows no such abuse of Rule 703. Rather, the alleged inadmissible evidence most often used under Rule 703 is hearsay, and we have clearly stated that such evidence is only admissible as a basis for expert opinion, not for any substantive value. See State v. Lundstrom, 161 Ariz. 141, 147-49, 776 P.2d 1067, 1073-75 (1989).

The court of appeals also argued that for the defense to effectively cross-examine the experts about their assumptions was “practically impossible without resorting to the precluded random match probability statistics.” While we note that Defendant effectively and thoroughly cross-examined the experts on the problems that may have occurred to taint the match they declared, we also find nothing under Rule 703 that would have precluded cross-examination to establish that the opinions were based on application of an unrecognized scientific principle. It is well established in Arizona that the basis for an expert’s opinion is fair game during cross-examination. See Ariz.R.Evid. 705; Arizona Evidence § 24, citing State v. Swafford, 21 Ariz.App. 474, 486, 520 P.2d 1151, 1163 (1974) (“The expert invites investigation into the extent of his knowledge, the reasons for his opinion including facts and other matters upon which it is based and which he took into consideration and may be subjected to the most rigid cross-examination concerning his qualifications and his opinion and its sources.”). Moreover, had Defendant still desired to keep out the numbers that were the basis for the experts’ opinions, he probably could have cross-examined the experts on the method of determining the significance of the match and the scientific controversy behind it without ever mentioning the exact numbers.

C. Exclusion of evidence of Mesa sexual assault

The trial judge rejected Defendant’s offer of evidence of another sexual assault with some similarities to the assaults charged in this case. Although police eliminated him as a suspect, Defendant argued that the perpetrator of the other sexual assault could have been the perpetrator in this case. The judge found that because of substantial differences between the two crimes, there was not enough evidence with an “inherent tendency to connect the other person with the actual commission of the [charged] crime.” Hummert, 183 Ariz. at 493-94, 905 P.2d at 502-03, citing State v. Oliver, 169 Ariz. 589, 590-91, 821 P.2d 250, 251-52 (App. 1991). Moreover, the judge held, on the basis of Rule 403, that the danger of confusing and misleading the jury outweighed the probative value of the evidence. See Ariz. R.Evid. 403. The court of appeals disagreed, holding that under Rule 404(b) (evidence of other acts admissible, inter alia, to show identity) the jury should have been allowed to hear the evidence and decide whether Defendant’s exculpation in the other case was relevant to the issue of identity in this case. Hummert, 183 Ariz. at 495, 905 P.2d at 504.

We do not believe the problem is grounds for reversal. Although this issue was not raised in the petition for review, we assume, arguendo, that the other act evidence was marginally relevant. Thus it was within the trial judge’s discretion to determine its admissibility under Rule 403. We see no abuse of discretion. Furthermore, given the overwhelming evidence of Defendant’s guilt, including the DNA evidence, any error in rejecting the other act evidence was, beyond a reasonable doubt, harmless.

D. Special concurrence

The rather unusual nature of the concurring opinion justifies brief comment. The concurring justice joined this court’s Bible and Johnson opinions. Now, although conceding the legal analyses and results were correct, he nevertheless wishes to confess some scientific errors in the language the court used in those cases to summarize scientific principles related to DNA typing, population genetics, and statistical analysis. Given the complexity of the science and mathematics underlying these principles, we readily concede that mistakes there may be — see ante, note 3 — but, as the concurring justice notes, those mistakes “did not affect the results.” Concurrence at 16.

We see no purpose therefore in proclaiming “mea culpa” for technical, scientific errors described in an as-yet unpublished law review article written by even the most distinguished law college professor. Respectfully, therefore, we decline to join in the concurring justice’s act of contrition. If, as the concurring justice believes, the trial court record in Bible showed that Cellmark’s “database was consistent with a population in Hardy-Weinberg equalibrium,” then so be it. Concurrence at 16.

Nor, despite the concurring justice’s view, did we attempt in past cases or this one to “resolve scientific issues.” Concurrence at 18. We attempt only to understand them, keeping in mind our lack of training in these disciplines, and to articulate them to the extent necessary to explain the reasons for concluding that a scientific principle has or has not been accepted in the relevant scientific community. It is hard to make such an explanation without stating at least the essence of the principle and explaining what is or is not accepted.

The law review article makes two proposals, both of which are explicitly or implicitly endorsed by the concurring justice. The first is that the courts should decide eases and write opinions without trying to explain the relevant scientific principles. The opinion would merely announce the result, based on scientific consensus, thus providing neither description nor explanation of what is or is not scientifically accepted. But as the author of the article himself acknowledges, that approach is “trivial” because it is “unlikely to produce convincing opinions.” As the author concludes, in the final analysis the court “must understand what needs to be understood,” and sometimes neither counsel nor the court’s own scientific research “provide[s] adequate clarification.” D.H. Kaye, Bible Reading: DNA Evidence in Arizona, 28 Ariz. St. L.J. 1035, 1073-74 (pre-publication copy).

The article’s second, and main, proposal is that the court should submit its draft opinions on cases involving scientific issues to a panel of learned scientists, who will undertake a sort of non-peer review process to make sure the court has correctly appreciated and decided issues affected by the sciences. Id. at 1075. Such a process would, of course, make life easier for the members of this court, but unlike courts exercising original jurisdiction, we have no provision for masters to vet draft appellate opinions. We hesitate to think of the comments from litigants and counsel who discover that their case has been effectively decided by an “impartial” group of scientists whose identity was not revealed to them, before whom they could not appear, and to whom they could address neither argument nor question.

CONCLUSION

We recognize that the passage of time has left us in a better position to evaluate the admissibility of DNA evidence than the courts considering the case before us. However, we hold here that the apparent trappings of science, the Frye rule, and scientific recognition need not cloud the courts’ views. Although compliance with Frye is necessary when the scientist reaches a conclusion by applying a scientific theory or process based on the work or discovery of others, under Rules 702 and 703 experts may testify concerning their own experimentation and observation and opinions based on their own work without first showing general acceptance. Such evidence need only meet the traditional requirements of relevance and avoid substantial prejudice, confusion, or waste of time. See Ariz. R. Evid. 403. The trial judge did not err in admitting the evidence in question in this case.

We therefore vacate the court of appeals’ opinion and affirm the trial judge’s rulings and Defendant’s convictions.

ZLAKET, C.J., and MOELLER, J., and JACOBSON, J. (Retired), concur.

ROBERT J. CORCORCAN, J.,

did not

participate in the determination of this matter; pursuant to Ariz.Const. art. VI, § 3, the Honorable EINO M. JACOBSON, J.(Retired) of the Arizona Court of Appeals, Division One, was designated to sit in his stead.

MARTONE, Justice,

concurring.

This is our third attempt to deal with the complexity of DNA. I write to suggest an approach that acknowledges our limitations. In State v. Bible, 175 Ariz. 549, 858 P.2d 1152 (1993), and State v. Johnson, 186 Ariz. 329, 922 P.2d 294 (1996), we worked hard to come to an understanding of a vast body of knowledge. Despite our genuine efforts, we now know that we misunderstood many intricate scientific principles. This is understandable — we are not trained scientists. Happily, our mistakes did not affect the results. But our reasoning was flawed by an imperfect understanding of the science of DNA. Two of many mistakes follow.

One reason we rejected statistical probabilities calculated using the product rule in Bible was that “the database relied on [was] not in Hardy-Weinberg equilibrium.” Bible, 175 Ariz. at 586, 858 P.2d at 1189. But in Bible, this perceived flaw would have benefited the defendant, and thus, was not a reason to exclude product rule estimates. David H. Kaye, Bible Reading: DNA Evidence in Arizona, 28 Ariz. St. L.J. 1035, 1055 (forthcoming 1997). Additionally, the expert testimony showed that the database was consistent with a population in Hardy-Weinberg equilibrium. Id. at 1056-57.

So too, in Johnson, we allowed expert testimony on the significance of a match using the modified ceiling method, in part because “the NRC report makes clear, the assumption of linkage equilibrium ... is well-grounded.” Johnson, 186 Ariz. at 332, 922 P.2d at 297. But the modified ceiling method was developed to be used in case linkage equilibrium did not exist. Kaye, supra at 1064^65. Because the modified ceiling method is generally accepted in the scientific community, we nevertheless reached the right result.

Notwithstanding these and other problems, the majority relies on Bible and Johnson as though we had not erred, and tries again to explain the science of DNA. I would not continue down this path. I believe it is time for us to acknowledge that it is neither necessary nor possible .for us to understand the science of DNA. It is enough that legitimate scientists do, and that DNA principles are generally accepted in the relevant scientific community.

We use the Frye standard under which the proponent of scientific evidence must establish that the underlying scientific principle is generally accepted in the relevant scientific community. Frye v. United States, 293 F. 1013, 1014 (D.C.Cir.1923). “Frye requires nothing more.” Fishback v. People, 851 P.2d 884, 891 (Colo.1993). Frye does not suggest that judges must become experts in the science behind the evidence. Rather, judges are to survey the relevant scientific literature, not for substantive content, but to determine the level of acceptance within the scientific community. We would not have erred in Bible had we stopped at the point of acknowledging that the product rule was not then generally accepted. We would not have erred in Johnson had we merely acknowledged that the modified ceiling method was.

Of course, a general understanding of the underlying science can only help the decision making process. But there are limits. It is not our task to resolve scientific issues. Nor should we presume to speak the vocabulary of science. I would leave the task of describing the details of new scientific principles to scientists.

In contrast, the question of admissibility is ours to make. We cannot delegate its resolution to scientists. There are two legal issues. The first is whether the DNA methodology used to determine a match satisfies Frye. The second is whether an expert may testify about the significance of a match, either quantitatively or qualitatively.

1. DNA methodology

The controversy that initially surrounded DNA typing has been resolved. Courts no longer question “[t]he biological and technological principles underlying the forensic methods for characterizing DNA variations.” National Research Council (NRC), The Eval nation of Forensic DNA Evidence 6-5 (1996) (prepublication copy).

In Bible and Johnson, we recognized the reliability of forensic DNA typing using the RFLP method. This case also involves the RFLP approach. “[T]he theory underlying DNA and RFLP technology is not generally open to serious attack----” State v. Moore, 268 Mont. 20, 885 P.2d 457, 468 (1994). Thus, the only unresolved issue in this case is whether expert testimony on the significance of a DNA match is admissible.

2. Expert interpretation of a DNA match

This court has twice addressed the second issue — the significance of a match. On both occasions, the controversy involved quantitative interpretations of the match.

In Bible, we decided that the product rule was not generally accepted at the time. Three years later, in Johnson, we held that the modified ceiling method was generally accepted in the relevant scientific community and, therefore, testimony on the statistical significance of a DNA match calculated under that method was admissible.

The product rule and the ceiling method are based on mathematical formulae. These in turn are based on statistics and population genetics. Brim v. State, at *2, 695 So.2d 268, 270 (Fla. Jan. 16,1997). Because the scientific community is in the best position to determine whether a formula is reliable, Frye governs. See id. at *3, at 270.

This case is unlike Bible and Johnson because it involves a qualitative, not quantitative, description of the significance of a match. The experts in this ease testified that they had never seen two samples from unrelated donors that matched over three probes, that the possibility of a random match was “rare,” and that DNA can “uniquely identify” a person. These conclusions were based upon their own scientific experience. Neither expert relied upon a controversial scientific principle. I agree with the court, therefore, that Frye is not applicable. The experts’ opinions concerning the “uniqueness of DNA” and their personal experience are admissible under Rule 702, Ariz. R. Evid. The data supporting them opinions are admissible under Rule 703, Ariz. R. Evid.

We are judges, not scientists. It is enough for us to be able to identify the legitimacy of a principle and its proponents so as to exclude junk science. Qualitative descriptions of the significance of a match are admissible. 
      
      . For a detailed explanation of RFLP analysis, the method used in this case, with cites to the scientific literature, see Bible, 175 Ariz. 549, 858 P.2d 1152; State v. Anderson, 118 N.M. 284, 881 P.2d 29 (1994).
     
      
      . See Frye v. United States, 293 F. 1013 (C.A.D.C. 1923), explained and applied in Bible, 175 Ariz. at 578, 858 P.2d at 1181.
     
      
      . The product rule is often described as simple multiplication of the frequency of the occurrence of- two alleles in the relevant population. For example, if when looking at one loci the profiles match and one allele is found in ten percent of the population and the other is found in fifty percent of the population, then the probability of a coincidental match is the product of the two frequencies. See Johnson, 186 Ariz. at 333 n. 3, 922 P.2d at 296 n. 3; Bible 175 Ariz. at 582, 858 P.2d at 1185. However, we made a mathematical error when explaining these calculations in Bible and Johnson. Because there are pairs of alleles, unless the alleles are identical the calculation should be 2(0.10 x 0.50) = 0.10, or a ten percent probability of a random match. National Research Council, The Evaluation of DNA Evidence 0-19 (1996).
     
      
      . In context, the 1992 Report stated:
      Can DNA typing uniquely identify the source of a sample? Because any two human genomes differ at about 3 million sites, no two persons (barring identical twins) have the same DNA sequence. Unique identification with DNA typing is therefore possible provided that enough sites of variation are examined.
      However, the DNA typing systems used today examine only a few sites of variation and have only limited resolution for measuring the variability at each site. There is a chance that two persons might have DNA patterns (i.e., genetic types) that match at the small number of sites examined. Nonetheless, even with today's technology, which uses 3-5 loci, a match between two DNA patterns can be considered strong evidence that the two samples came from the same source.
      Interpreting a DNA typing analysis requires a valid scientific method for estimating the probability that a random person might by chance have matched the forensic sample at the sites of DNA variation examined. A judge or jury could appropriately weigh the significance of a DNA match between a defendant and forensic sample if told, for example, that "the pattern in the forensic sample occurs with a probability that is not known exactly, but is less than 1 in 1,000” (if the database that shows no match with the defendant’s pattern is of size 1,000).
      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 might occur by chance, is meaningless.
      1992 Report, at 74. We read this to mean that there should be some analysis of the significance of the match, but it does not direct the method by which the significance should be expressed.
     
      
      . Frye does not ask judges to engage in a numbers game. General acceptance is determined by considering “the quality, as well as quantity, of the evidence supporting or opposing a new scientific technique. Mere numerical majority support or opposition by persons minimally qualified to state an authoritative opinion is of little value....” People v. Leahy, 8 Cal.4th 587, 34 Cal.Rptr.2d 663, 882 P.2d 321, 336-37 (1994).
     
      
      . I recognize that some cases may require the court to give a very basic overview of the underlying science. The present case, however, does not hinge upon scientific principles. This case involves the Rules of Evidence, not the application of a scientific principle. See infra at 128-129, 933 P.2d at 1196-97. The court's explanation of forensic DNA typing is, therefore, unnecessary. See ante at 122-123, 933 P.2d at 1190-91.
     