DocketNumber： C017199
Judges： Nicholson
Filed Date： 3/15/1995
Status： Precedential
Modified Date： 11/3/2024
Court of Appeals of California, Third District.
*77 COUNSEL
Daniel E. Lungren, Attorney General, Roderick E. Walston, Chief Assistant Attorney General, Carol Ann White and Mary Jane Hamilton, Deputy Attorneys General, for Plaintiff and Appellant.
Howard M. Hoffman for Defendant and Respondent.
OPINION
NICHOLSON, J.
A woman has intercourse with several different men and conceives a child. Years later, she identifies one man as the father and blood tests show this man closely matches the genetic characteristics expected of the child's father. By statute, these test results trigger a presumption of paternity. (Fam. Code, § 7555; former Evid. Code, § 895.5.) The other men are not tested. We conclude evidence of the mere existence of other, untested, men is insufficient of itself to rebut the statutory presumption of paternity based on genetic testing.
The Attorney General prosecutes this appeal from an adverse ruling dismissing a paternity complaint. We construe the premature notice of appeal from this nonappealable ruling to encompass the judgment. (9 Witkin, Cal. Procedure (3d ed. 1985) Appeal, § 414, pp. 411-413.) We need address but one of the arguments: whether substantial evidence supports the trial court's decision. On this question we disagree with the reasoning and analysis proffered by the Attorney General, but we agree no substantial evidence supports the judgment. We reverse with directions.
The specifics of the testimony will be revisited later, after a discussion of the scientific significance of it. However, to provide context we offer the following precis: The child was born on October 17, 1982. The mother had sex with defendant around the time of the Pig Bowl, which was played on January 23, 1982, about nine months before. (See fn. 3, post.) The trial court's opinion is muddled on this point, but the statement of facts in defendant's respondent's brief states without qualification that the mother had intercourse with him during the period of conception. Defendant is bound by this concession. (Mangini v. Aerojet-General Corp. (1991) 230 Cal. App.3d 1125, 1152 [281 Cal. Rptr. 827]; Federer v. County of Sacramento (1983) 141 Cal. App.3d 184, 186 [190 Cal. Rptr. 187]; 9 Witkin, Cal. Procedure, op. cit. supra, § 482, pp. 472-473.) There was evidence that *78 during that period the mother may have had sex with three other men. Based on certain blood tests, when comparing defendant to a random man there was a 99.69 percent relative chance he was the father, even assuming the mother had three other sex partners. Defendant's "paternity index" was 970, more than enough to trigger a statutory presumption of paternity.
Some knowledge of the science underlying genetic testing is necessary to understand the legal issue raised in this case. "In a paternity trial, a fact-finder is naturally tempted to seize upon statistical figures, like the paternity index or the probability of paternity, as lifelines of objective truth in a sea of prevarication. ``Soft' evidence involving difficult questions of credibility and other circumstantial matters may be submerged or lost because it appears unnecessary to resolve the questions in light of the hard, scientific, mathematical proof. Under these circumstances it is absolutely essential that the significance of the mathematical proof be clearly understood by both counsel and the fact-finder." (Peterson, A Few Things You Should Know About Paternity Tests (But Were Afraid to Ask) (1982) 22 Santa Clara L.Rev. 667, 684, fn. omitted (Peterson).)
Through testing of blood and tissue, particularly HLA (human leukocyte [white blood cell] antigen) testing, certain genes can be identified. If a child has a gene not contributed by the mother, it was contributed by the father. If a man could not have contributed the gene, he is not the father. But the converse is not true; merely because he could have contributed the gene does not prove the man is the father. Thus, genetic testing alone cannot establish paternity. By itself, at most it can only preclude paternity. (See Comment, DNA Fingerprinting and Paternity Testing (1989) 22 U.C. Davis L.Rev. 609, 614.)
Certain genes are more or less common in given human populations. If the putative father possesses uncommon genes which must have been contributed by the child's father, often it is said there is a greater likelihood or probability he is the true father, expressed as a high paternity index or "probability of paternity." (DNA Fingerprinting and Paternity Testing, supra, 22 U.C. Davis L.Rev. at pp. 616-617.) But the assumption misleads. (Peterson, supra, 22 Santa Clara L.Rev. at pp. 669, 685.) This "likelihood" exists only because we assume the man had what is obliquely referred to as "access *79 to the mother." (E.g., In re Paternity of M.J.B. (1988) 144 Wis.2d 638 [425 N.W.2d 404, 409].) Regardless of the genetic makeup of the putative father, if he is infertile or did not have access to the mother, he is not the father. Without access there can be no paternity. (Id. at p. 410.) (1) The trier of fact cannot find a defendant is the father based solely on expert testimony. Such testimony must be coupled with so-called "nongenetic" testimony ("soft" evidence) establishing access.
A joint committee of the American Bar Association and American Medical Association promulgated certain guidelines which, in combination with standards set by the American Association of Blood Banks (AABB), create the backdrop for expert testimony in a particular case. (Joint AMA-ABA Guidelines: Present Status of Serologic Testing in Problems of Disputed Parentage (1976) 10 Fam. L.Q. 247 [hereafter Guidelines]; see generally, Walker, Inclusion Probabilities in Parentage Testing (1983).) A brief explanation of certain terms follows.
The probability of exclusion (or "prior probability of exclusion") is "the probability that the tests employed will exclude a falsely accused man. If the probability of exclusion with the tests employed is 95 percent, of 100 non-fathers 95 will be excluded and 5 will not be excluded.... This does not mean that there is a 95 percent chance that the alleged father is the true father.... [T]here is no direct relationship between the probability of exclusion and the likelihood of paternity. Likelihood of paternity cannot be extrapolated from the probability of exclusion.... The significance of the probability of exclusion is that if he is not excluded as a possible father, the likelihood of paternity can be estimated by considering other available empirical evidence." (Division of Family Services v. Guffey (Mo. App. 1990) 795 S.W.2d 546, 548, fn. 2, italics omitted (Guffey.) Confusingly, a separate "probability of exclusion" is specific for the given mother-child combination. (Peterson, supra, 22 Santa Clara L.Rev. at p. 679; see Reisner & Bolk, A Layman's Guide to the Use of Blood Group Analysis in Paternity Testing (1981-1982) 20 J. Fam. L. 657, 671 [hereafter A Layman's Guide].)
The paternity index, sometimes called the "likelihood ratio," or "chance (or likelihood) of paternity," "involves the probability that a cross between the [putative father] and the mother would produce an offspring with the child's phenotypes and the corresponding probability for a random selection of genes from the male population." (Kaye, Plemel as a Primer on Proving Paternity (1988) 24 Willamette L.Rev. 867, 877 [hereafter Proving Paternity].) "Despite the alternative labels, it is not the probability that the accused is the father." (Plemel v. Walter (1987) 303 Ore. 262 [735 P.2d 1209, 1213], italics in original (Plemel); see Guffey, supra, 795 S.W.2d at p. 549, fn. 2.) *80 The chance of paternity is the paternity index converted into a percentage.[1] (Plemel, supra, 735 P.2d at p. 1214.)
The probability of paternity (or "posterior probability of paternity") is the probability the putative father is the true father of the child in question, and is a term often misused and misunderstood. The probability of paternity must take into account the "soft" or "nongenetic" evidence in the case. Such "soft" evidence is converted into a figure known as the "prior chance" or "prior probability of paternity." For example, if but one man had access to the mother, his prior probability of paternity (the probability of paternity without considering the genetic evidence) would be 100 percent. His posterior probability of paternity (the probability after considering the genetic evidence) would also be 100 percent, because the "soft" evidence establishes paternity, regardless of the genetic evidence. If a man had no access to the mother, his prior probability of paternity would be zero, as would his posterior probability of paternity. Again, regardless of the genetic evidence, the nongenetic evidence establishes nonpaternity. (Plemel, supra, 735 P.2d at p. 1215.)
But the nongenetic evidence is never this simple. In most cases the trier of fact has some evidence of access and some evidence of nonaccess. "Since these absolutes cannot be known, we can estimate these values as 90 percent for a strong pro-paternity case and 10 percent for a weak case. Traditionally, laboratories use a neutral figure of 50 percent in their calculations. When 50 percent is used, the likelihood of paternity is mathematically identical to the probability of paternity. Hence when laboratories ignore the prior probability they are assuming it is 50 percent, a figure which may or may not be appropriate." (A Layman's Guide, supra, 20 J. Fam. L. at p. 674; see Proving Paternity, supra, 24 Willamette L.Rev. at pp. 878-881.)
Use of the 50 percent figure means it is as likely the putative father had access to the mother as the random man. Some courts view this assumption of equal access as an impermissible evidentiary presumption which deprives the defendant of due process. (See State v. Skipper (1994) 228 Conn. 610 [637 A.2d 1101, 1103-1108] [criminal conviction reversed because testimony assumed intercourse took place]; In re Paternity of M.J.B., supra, 425 *81 N.W.2d at p. 409; but see State v. Spann (1993) 130 N.J. 484 [617 A.2d 247, 253] [no such presumption arose]; Kammer v. Young (1988) 73 Md. App. 565 [535 A.2d 936, 941] [use of equal chance is neutral].) The better practice may be for the expert to testify to a range of prior probabilities, such as 10, 50 and 90 percent, and allow the trier of fact to determine which to use. (Plemel, supra, 735 P.2d at p. 1219; Peterson, supra, 22 Santa Clara L.Rev. at p. 691, fn. 74; see M.J.B., supra, 425 N.W.2d at pp. 410-411; State v. Jackson (1987) 320 N.C. 452 [358 S.E.2d 679, 682]; Kammer, supra, 535 A.2d at p. 942.)
We need not enter into this quagmire because this precise point is not raised on appeal. But it emphasizes the importance of understanding expert testimony cannot supplant evidence of access; expert testimony must be viewed through the lens provided by the soft evidence. (2) Accordingly, an expert "is unqualified to state that any single figure is the accused's ``probability of paternity' ... [because] such a statement requires an estimation of the strength of the other evidence presented in the case ..., an estimation that the expert is in no better position to make than the trier of fact."[2]
With this understanding of the testing nomenclature, we consider the effect of a statute on the meaning of the scientific testing.
The usual paternity suit involves a man, hereafter referred to as the defendant, who does not wish to be declared the father of the child. Because of the accuracy and statistical significance of modern blood testing, the California Legislature has adopted a statutory presumption of paternity. If the defendant's blood test results in a particular numerical score, he is presumed to be the father. Family Code section 7555 (former Evid. Code, § 895.5) provides in relevant part: "(a) There is a rebuttable presumption, affecting the burden of proof, of paternity, if the court finds that the paternity index, as calculated by the experts qualified as examiners of genetic markers, is 100 or greater. This presumption may be rebutted by a preponderance of the evidence."
The express legislative intent was "to standardize the process by which paternity is established in order to achieve a greater degree of equity and consistency in paternity determinations. The Legislature finds that the science of genetic testing has advanced to the degree that paternity determinations resulting from such testing are so reliable that the burden of proof can be shifted to the putative father." (Stats. 1986, ch. 629, § 1, pp. 2136-2137.)
The defendant is entitled to introduce other expert testimony. (Fam. Code, § 7557.) Once the statutory presumption is triggered, the court must consider all of the evidence, including any blood test evidence. (Fam. Code, § 7554, subd. (b).) The statutory presumption "may be rebutted by a preponderance of the evidence." (Fam. Code, § 7555, subd. (a).)
(3) The Attorney General argues the statutory presumption is not only triggered by a paternity index of 100, the presumption is strengthened as the index rises. In his view, the degree of proof needed to rebut the presumption rises with the index, requiring a defendant with a very high index to produce "unusually strong contradictory evidence" or "truly extraordinarily strong and reliable evidence." This can be pictured as a line curving asymptotically toward another ever closer but never reaching. The Attorney General's *83 picture is out of focus: The Legislature has stated the requisite standard of proof in the statute: preponderance of the evidence.
(4) The statute, Family Code section 7555, does not specify what classes of evidence may be used to rebut the presumption. In our view, the defendant may avail himself, inter alia, of impeachment and rebuttal of expert testimony.
First, if the defendant introduces evidence the expert testing was conducted improperly, or the wrong gene frequency table was used, or the opposing expert is biased, the defendant may demonstrate his paternity index is not 100 or more. For example, a defendant may prove he is excluded genetically by a test performed by his expert but not considered by the opposing expert or that his paternity index is only 99 or less. Such evidence, if believed, undermines the presumption itself.
Second, the defendant may prove he is infertile or otherwise had no access to the mother during the period of conception. (See Matter of C.M.C. (1990) 155 Wis.2d 331 [455 N.W.2d 248, 249, 250] [fact finder could find birth control during intercourse established nonaccess].) Such evidence establishes the defendant's prior probability of paternity is zero and, hence, shows nonpaternity.
Third, a defendant might prove another man who had access to the mother also has a high paternity index, which would raise a competing or "inconsistent" presumption. (See 1 Witkin, Cal. Evidence (3d ed. 1986) Burden of Proof and Presumptions, § 274, p. 234.) For example, two related men could have access to the mother. (See 1 McCormick on Evidence (4th ed. 1992) Experimental and Scientific Evidence, § 211, pp. 959-960 [Talmudic problem of widow marrying brother in-law too soon and giving birth six months later].) Or a woman may not know with which of two related men she had intercourse. (See, e.g., D. Cronenberg, Dead Ringers (U.C.L.A. Film-T.V. 1988).) The so-called "hard" scientific testing could result in competing presumptions of paternity which canceled each other out, relegating the trier of fact to the "soft" evidence. (See Teraski, Resolution by HLA Testing of 1000 Paternity Cases Not Excluded by ABO Testing (1977-1978) 16 J. Fam. L. 543, 549.)
But what if the other man is dead, missing, or unknown? Except in the rare case where he left behind a blood or tissue sample, his paternity index *84 is unknown and hence, no different from the random man's index. For this reason, evidence of access by one untested man does nothing to rebut the statutory presumption. Such evidence does not alter the defendant's paternity index. (See Proving Paternity, supra, 24 Willamette L.Rev. at p. 882.) Nor does it change his prior or posterior probabilities of paternity.
The value of "other man" evidence is limited. Tested and excluded "other men" fall out of the equation. A tested, included man may raise a competing presumption if his paternity index is high enough. But in most cases which involve a high paternity index, testimony about an untested man or untested men will not be very important because proof of access by several untested men may not alter significantly the probability of paternity. (See fn. 2, ¶ 3, ante.)
Our conclusion is in accord with Jones v. Crawford (Fla. Dist. Ct. App. 1989) 552 So.2d 926, wherein the mother testified she had sex with Crawford and another man during the period of conception. The other man was not tested, but Crawford's test showed a 98.23 percent probability of paternity. Under the Florida statute, this created a rebuttable presumption of paternity. "The trial court recognized the [statutory presumption] but found that [the mother's] credibility was questionable and that [she] received a military allotment from the other man while he was in the service. On these findings, the court ruled that [Crawford] had rebutted the statutory presumption." (552 So.2d at p. 927, fn. omitted.) The Florida appellate court reversed: "In the instant case, [Crawford] failed to meet the burden of overcoming the presumption. [He] did not demonstrate that the HLA test results were erroneous, did not avail himself of the procedures for retesting ... and did not submit evidence tending to prove that, for any reason (such as sterility or total lack of access), he could not have been the father. Absent such evidence, [his] bare denial and testimony that someone other than [himself] had sexual relations with the mother did not overcome the presumption established by the HLA test results and Section 742.12(1), Florida Statutes (1987)." (Id. at p. 928.)
We do not imply that under California law a defendant's "bare denial" of intercourse would be insufficient, even if believed by the trier of fact. But Jones is correct insofar as it establishes a defendant must produce some sort of evidence which rebuts the presumption, and in the usual case, "other man" evidence is not enough.
(5) Of course, we must view the evidence in the light most favorable to the trial court's ruling. "To be considered substantial, evidence must be *85 ``"of ponderable legal significance ... reasonable in nature, credible, and of solid value...."'" (Pacific Gas & Electric Co. v. Zuckerman (1987) 189 Cal. App.3d 1113, 1134 [234 Cal. Rptr. 630], citations and internal quotation marks omitted.) All reasonable inferences must be drawn in favor of the judgment. (People v. Barnes (1986) 42 Cal.3d 284, 303-304 [228 Cal. Rptr. 228, 721 P.2d 110]; People v. Johnson (1980) 26 Cal.3d 557, 562 [162 Cal. Rptr. 431, 606 P.2d 738, 16 A.L.R.4th 1255]; Overton v. Vita-Food Corp. (1949) 94 Cal. App.2d 367, 370 [210 P.2d 757].) But "reasonable" inferences do not include those which are contrary to uncontradicted evidence of such a nature that reasonable people would not doubt it. (Gaffney v. Downey Savings & Loan Assn. (1988) 200 Cal. App.3d 1154, 1168 [246 Cal. Rptr. 421].) And scientific or expert evidence must be evaluated in light of the factors considered and the reasoning employed. (See Zuckerman, supra, 189 Cal. App.3d at p. 1135.)
"Under the often-enunciated rule, which is so often forgotten in the enthusiasm of advocacy, we look to the evidence accepted by the trial court." (Findleton v. Taylor (1962) 208 Cal. App.2d 651, 652 [25 Cal. Rptr. 439].) We disregard the Attorney General's editorial comments about the facts, such as the repeated reference to the child as "young Johnny," the unsupported claim the mother was badgered in the trial court, and the assumption the defendant must be the father because he opposed DNA testing of his person. We previously denied the Attorney General's request to consider evidence not introduced at trial. In a supplemental brief, the Attorney General makes further factual assertions which we disregard.
(6a) The mother had engaged in intercourse with Bill Krueger in December 1981, but could not remember the last time. Until recently she thought John Utley was the father of the child, "[a]nd the only other person that I had been with at all was Bill Misura, and our first date was the Pig Bowl." She first had sex with defendant the evening of the Pig Bowl.[3] She testified this was around January 22, 1982. She had intercourse with him on one other evening, for a total of five times on two evenings. She had thought she might already be pregnant by Utley, but despite this belief, she later told defendant she was pregnant and he offered to pay for one-half of the abortion costs. After she decided not to abort the child, the mother continued to have intercourse with Utley. She changed her belief about paternity when she received a laboratory report which excluded Utley as the father. In a *86 1982 child support document, she claimed one "Steve" was the father, but she testified this was a lie. In other documents she claimed Utley was the father.
To the extent the Attorney General believes no reasonable inference could be drawn the mother had intercourse with other untested men, he is mistaken. From the evidence presented, the trial court could find the mother had intercourse with defendant, Krueger, "Steve" and Utley.
An expert, Dr. Julita Fong, testified Utley was not the father. Defendant had a paternity index, as defined by statute, of 970. "[P]aternity is practically proved."[4] When comparing defendant to a "random man," there was a 99.69 percent relative chance defendant was the father, even assuming the mother had three other sexual partners. Assuming but one other partner, the relative chance was 99.90 percent.
Defendant did try to prove through cross-examination that he was missing a particular gene which the father had to have, but the evidence included testimony explaining one of the tests was invalid and Dr. Fong opined defendant did have the gene in question, as reflected on two other runs of the same test.
Although defendant was permitted to produce other expert testimony (Fam. Code, § 7557), he did not. Accordingly, the question of paternity was "submitted upon all the evidence, including evidence based upon the tests" in accordance with Family Code section 7554, subdivision (b).
On appeal, the parties disagree about the strength of the medical testimony, but the trial court's findings state: "The testimony of Dr. Fong established a rebuttable presumption of paternity regarding the defendant. Her findings are found to be valid and well established in scientific methodology. Her testimony is entirely believable." This finding stands unassailed and, therefore, with one exception we need not delve further into the complexities of the testimony.
(7) Defendant's principal argument on appeal relates to a snippet of Dr. Fong's testimony: "The trial court stated it found Dr. Fong's testimony *87 entirely believable. Dr. Fong specifically testified that there was only a 46.28 percent likelihood that respondent had the necessary genes to be capable of fathering this child.... This testimony alone is sufficient to uphold the judgment."
We disagree. The trial court's statement that it found Dr. Fong's testimony credible works to defendant's disadvantage, because that testimony, taken as a whole, establishes the requisite paternity index, which the trial court found had been established. The portion of the testimony defendant points to is taken out of context. Dr. Fong testified this 46.28 percent "likelihood that [defendant] contributed the necessary genes to be the father" must be combined with "how likely it is that a ``random man' would contribute the necessary genes to be the father [in order] to achieve the combined paternity index and the relative chance of paternity." That is consistent with our previous explanation of the need to use a "random man." (See p. 79 & fn. 2, ¶ 2, ante.) The trial court specifically asked whether this figure meant there was less than a 50 percent chance "that [defendant] was in fact the person that contributed the genes," to which Dr. Fong replied no. If and only if Dr. Fong ignored the "random man," which accounts for the frequency of genes in the relevant population, would the number bear the meaning defendant attributes to it.
(6b) Because Utley is excluded by the medical evidence, which the trial court accepted, we are concerned only with the other two men, "Steve" and Krueger, plus a "random" man. When Dr. Fong testified defendant has a 99.69 percent chance of being the father, she assumed it was equally likely all four men (defendant, "Steve," Krueger and the random man) were the father. The paternity index, divided by the paternity index plus three ("Steve," Krueger and the random man) equals the (posterior) probability of paternity. (See fn. 2, ¶ 2, ante.) In this case, 970 divided by 973 equals 99.69 percent, as Dr. Fong testified. Thus, given that the trial court credited the medical testimony, the presence of other, untested men does not aid in rebutting the presumption.
The trial court found "the testimony of and documentary evidence presented through [the mother] causes the court to find that the presumption of paternity has been rebutted by a preponderance of the evidence. [¶] Significant factors considered were the great number of conflicting statements regarding sexual partners by [mother] and the great passage of time which contributed to failure of memory and conflicting statements about dates and times."
We do not construe the court's findings to mean it disbelieved the mother's testimony she had intercourse with defendant during the period of *88 conception. The court stated at the outset the mother had had "casual relations" (i.e., sexual congress) with defendant, Utley, and Krueger, but that she was imprecise about when. Unless the court believed defendant had access to the mother, it had no cause to invoke the presumption. (See pp. 78-79, ante.) Moreover, as stated earlier, defendant concedes he did have intercourse with the mother during the period of conception. We infer the court found "Steve" existed. Assuming Utley is excluded as the father, the record shows the father could be Bill Krueger, "Steve," or defendant. Viewing the evidence in the light most favorable to the judgment, each of these men had sexual congress with the mother around the time of conception.
The trial court took the view the mother's conflicting statements and poor memory of dates means it is equally likely any of these men could be the father, and therefore the presumption was rebutted. However, the putative father bore the burden to rebut the presumption of paternity. Therefore as a matter of law it was not equally likely any of the men could be the father. Due to the results of the genetic testing, which established a paternity index of 970, defendant was presumed the father. Defendant produced no evidence of impotence or sterility, no evidence he did not have sexual congress with the mother (in fact, he concedes that he did), and no expert evidence controverting the "match" found by Dr. Fong. He produced no evidence that any other man who had access to the mother during the period of conception had been tested and found to have a "match." The evidence left is that the mother had sex with two untested, unexcluded, men during the period of conception. This evidence is insufficient to rebut by a preponderance of the evidence the statutory presumption of paternity.
The trial court's finding is irreconcilable with the facts. Defendant had intercourse with the mother during the period of conception and has more than the necessary blood characteristics to trigger the statutory presumption of paternity. The trial court accepted the medical evidence. The trial court's conclusion the existence of other, untested men rebutted the presumption is not correct. Although the mother had difficulty remembering when she had intercourse with which men, that does not affect the fact she had intercourse with defendant during the period of conception and does not rebut the presumption. The statutory presumption stands unrebutted. Defendant is the father.
The judgment is reversed with directions to the trial court to enter a judgment of paternity. Costs to appellant.
Blease, Acting P.J., and Sims, J., concurred.
A petition for a rehearing was denied April 11, 1995, and the opinion was modified to read as printed above. Respondent's petition for review by the Supreme Court was denied June 13, 1995. Mosk, J., and Kennard, J., were of the opinion that the petition should be granted.
[1] The Guidelines attach the labels "practically proved," "extremely likely," "very likely," "likely," "undecided," and "not useful" to various percentage ranges. (See Guidelines, supra, 10 Fam. L.Q. at p. 262.) However, "[t]hese terms have no objective scientific status, and supply no information that the probability of paternity does not supply more precisely." (Proving Paternity, supra, 24 Willamette L.Rev. at p. 882; see also id. at p. 883 and fn. 62.) At least one court has held such "verbal predicates" are inadmissible, because they are misleading to the fact finder. (Plemel, supra, 735 P.2d at p. 1219; see id. at p. 1214, fn. 5.) We agree.
[2] (Plemel, supra, 735 P.2d at p. 1217.) An example will help illustrate these concepts. In Plemel, the tests showed a prior probability of exclusion of 97.5 percent. (Id. at p. 1211.) The putative father (Walter) had a paternity index of 178. This means "that it is 178 times more likely that a union of Plemel and Walter would produce a child with the observed [genetic] markers than would a union of Plemel and a set of [paired genes] picked at random from men of Walter's race." (Proving Paternity, supra, 24 Willamette L.Rev. at p. 874.) This is converted into a chance of paternity of 99.4 percent (178 divided by 1 + 178 = .9944). (Ibid.; see Plemel, supra, 735 P.2d at p. 1214.) Although the expert did not express a probability of paternity as such, by inference he assumed a prior probability of paternity of 50 percent, and the (posterior) probability of paternity was 99.4 percent. (Id. at p. 1215.)
"It can be mathematically shown [sic] that the index of a random man is one. Since one random man is equally as likely as another random man to have fathered the child, this conclusion is also intuitively clear. It can also be shown that if more than one man is possibly the father, and if each man is equally as likely to have fathered the child as any other, then the probability that any one of the men is the father is equal to his paternity index divided by the sum of the indices of all of the possible fathers." (Peterson, supra, 22 Santa Clara L.Rev. at p. 686, fns. omitted.)
A probability of paternity for Walter of 99.4 percent is determined by dividing his paternity index by the sum of his index plus the random man's index, or 178/ (178+1) or .9944. If it were certain two men had access to Plemel besides Walter, Walter's paternity index would still be 178. But the probability of paternity would be 178 divided by 178 plus 2. That would be.9888 or 98.9 percent. Therefore, in Walter's case, proof of access by two untested other men would not indicate nonpaternity. Even if Plemel had intercourse with five untested men besides Walter, his posterior probability of paternity would still be 97.3 percent (178/ (183) = .9726).
[3] The "evening of" the game would be January 22, 1982, as she estimated. We take judicial notice that Pig Bowl VIII was played on January 23, 1982 (Evid. Code, § 452, subd. (h)): the Bacon Bombers (police) beat the Razorbacks (sheriffs) 14-12. (See Sacramento Bee (Jan. 20, 1982) p. C2, (Jan. 24, 1982) pp. B1, C1; Sacramento Union (Jan. 23, 1982) p. D1, (Jan. 24, 1982) p. C1.)
[4] When Dr. Fong testified paternity was "practically proved," she was using one of the discredited "verbal predicates" promulgated by the scientific community and was not expressing her belief, as an expert, that it was "practically proved" defendant was the father. (See fn. 1, ante; see also Plemel, supra, 735 P.2d at pp. 1214, fn. 5, 1219 [use of this phrase before jury is prohibited].)