OPINION OF THE COURT
I. FINDINGS OF FACT AND CONCLUSIONS OF LAW
In this paternity proceeding, petitioner Department of Social Services is the assignee of Sara H. and seeks to establish that respondent Bart D. is the father of Ms. H.’s child, Alexandra, born August 26, 1981, and seeks to compel respondent to furnish support for the child. The respondent denied paternity. The court ordered a human leucocyte antigen blood test (HLA test), and the matter proceeded to a full hearing which was completed on August 15, 1983.
For the reasons summarized below, the court finds by evidence that is clear, convincing, and entirely satisfactory, if not overwhelming, that respondent is the father of the child Alexandra.
*426Petitioner’s principal witness was Ms. H. She testified that she met the respondent, a police officer, at a restaurant in Manhattan. Ms. H. further testified that she first had sexual relations with the respondent at a Manhattan motel on the afternoon of November 13, 1980, and on two subsequent occasions. About the beginning of 1981 she learned she was pregnant, and repeatedly contacted the respondent concerning her pregnancy and the later birth. She denied having had sexual relations during the period August, 1980 through the end of December, 1980, with anyone other than the respondent. Petitioner called one other witness who corroborated aspects of Ms. H.’s testimony.
In observing Ms. H.’s demeanor and in listening to her testimony the court found her to be a highly credible witness.
Petitioner introduced into evidence the results of the HLA test, which test was performed at the Lindsley F. Kimball Research Institute of the New York Blood Center. The test results calculated the “plausibility of paternity” at 99.2%, and that it was therefore “extremely likely” that the respondent was the father of the subject child.
Respondent’s case consisted of respondent’s testimony and the testimony of Mr. Joseph V. Respondent also called Dr. Leon Sussman, the director of the facility that performed the HLA test. Respondent testified that he met Ms. H. in the summer of 1980, and acknowledged in his direct testimony that he had sexual relations with Ms. H. Respondent testified, however, that he had sexual relations with Ms. H. only once, and that the date of the sexual act was sometime in late August or September of 1980. Respondent denied having had sexual relations with Ms. H. other than on that one occasion, and categorically denied having had sexual relations on November 13, 1980, or thereafter. Respondent also introduced in evidence a so-called “command log” of the precinct where he was assigned in an attempt to cast doubt as to whether he could have had sexual relations with Ms. H. at the time and place she so testified. Mr. V. testified that he dated Ms. H. and, contrary to Ms. H.’s testimony, had sexual intercourse with her. Although the respondent called Dr. Sussman as *427his witness, Dr. Sussman’s testimony fully substantiated the accuracy and weight of the HLA test performed at his laboratory. The doctor explained the process by which the blood is drawn and tested for paternity. Dr. Sussman explained that álthough no blood test can determine paternity with an absolute 100% certainty, that in this case the odds were, in effect, highly certain that respondent was the father of the subject child. In addition, Dr. Sussman made it clear that in this case the race of the mother, or her racial ancestry, would make no difference in the degree of certainty in calculating the likelihood of paternity.
In observing the respondent’s demeanor and in listening to his testimony, the court found his credibility to be low and disbelieves the essentials of his testimony. In addition, the court found Mr. V.’s testimony, based on both his demeanor and on the content of his testimony, including his business and personal connection's with respondent, devoid of credibility. The court further finds the police precinct command logs introduced in evidence to be of little value in establishing respondent’s whereabouts on November 13, 1980. With respect to the logs, respondent attempted to show that an entry was made in the November 13, 1980 10th Precinct log, which would have placed him on duty at the precinct station at the time he was allegedly having sexual relations with Ms. H. However, not only was there scant testimony concerning the general accuracy of entries in logs of this type, but it is clear to the court that respondent had not only continuous access to the particular log in question, but also a substantial motive to control, if not distort or fabricate, such entries to his benefit.
Accordingly, the court resolves the disputed testimony between Ms. H. and the respondent concerning the specific date the two had sexual relations in favor of Ms. H., and the court therefore finds as a fact that respondent had sexual relations with Ms. H. at a time consistent with the resulting date of birth of the child.
In summary, Ms. H.’s credible testimony, the results of the HLA test, which the court gives substantial weight, and respondent’s own admission of having met and had sexual relations with Ms. H., all combine to provide overwhelming evidence that respondent is the father of the *428child Alexandra. (See Matter of Alicia C. v Evaristo G., 93 AD2d 820.)
II. respondent’s argument concerning evidentiary VALUE OF HLA TESTS
Respondent requested and was granted an opportunity to submit a memorandum to the court in lieu of closing oral argument. In his memorandum respondent, inter alia, attacks HLA test results in general and in this specific instance as “meaningless”. Because respondent sets forth a statistical argument that manages to combine both superficial plausibility with patent error, it is worth commenting upon. It appears that arguments similar to that contained in respondent’s memorandum are being raised with increasing frequency in paternity actions, as the frequency of HLA testing has correspondingly increased. (See Lauter, Paternity: The Final Word, National LJ, Sept. 12, 1983, p 1.)
To quote from respondent’s memorandum:
“The submission of the results of the HLA test alone does not provide evidence to any degree whatsoever that the Respondent is in fact the father of the child. To accept the mere test results alone without some expert testimony correlating the test results with the existential evidence in this case is a meaningless exercise. In a paternity trial the fact finder is naturally tempted to seize upon statistical figures, like the probability of paternity, as lifelines of objective truth in a sea of lies. ‘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.
“The paternity index, and the probability based upon it, can be easily misused. Taking the example of the man with a probability index of 99.5, it is clear that in a large population many men will have a phenotype compatible with fathering the child. If only one man in a thousand were to have the proper phenotype, there could be 1000 men who could have fathered the child in an urban popula*429tion containing only one million men.* There is no way to tell which of these 1,000 men is the father. The most that the HLA evidence can tell is that, assuming paternity is limited to the men in this city and the Respondent is one of them, his probability of paternity is only one in a thousand, or .1%.
“The HLA test results merely represents the likelihood that a man with the phenotype of the Respondent would contribute the required genes compared with the likelihood that a random man of the same ethnic group would do so. In order to convert this figure into the actual probability of paternity, the Court must also consider the probability that the Respondent had intercourse once at the right time to impregnate the Petitioner. If the Respondent had no intercourse at the right time, then, regardless of the test number, his probability of paternity is zero.
“That is why when Dr. Sussman was asked to state whether the HLA test proved that Sergeant D. was the father of the child he unequivocably stated that it absolutely did not. Furthermore, Dr. Sussman testified that the HLA test did not, nor could it prove that Sergeant D. was the father of the child. All that the test could show was that the Respondent was 1 out of 125 men who had a similar phenotype. This is not evidence in a city where there are 5.000. 000 men.
“The Court should totally reject the HLA evidence because standing alone it proves absolutely nothing. In order for the test results to have any fair meaning another step was required such as producing an expert to apply the results of the HLA test together with the existential evidence and to base an opinion Upon a theory such as Bayes’ Theorem. Without this additional step the Court should entirely reject the HLA test because it is truly unfair evidence and does not prove what it appears to prove..” (Emphasis added.)
Respondent, using statistical artifice, totally misconstrues the role of HLA evidence in a case of this type.
Dr. Sussman testified that the 99.2% “plausibility of paternity” leading to the conclusion that paternity was “extremely likely” meant that the odds were 126/1 that a *430randomly selected male from the general population with the respondent’s blood type could be the father of the subject child. Respondent notes that, given the large male population in New York City, many thousands of men could potentially be the father of the child. Respondent’s premise, namely, that the HLA test can only narrow down the list of potential paternity candidates is correct. But his leap to the conclusion that “This is not evidence in a city where there are 5,000,000 men” is erroneous. Respondent alludes to his own misconception when he suggests that what is necessary is that “an expert” (presumably a statistician), should apply the HLA test results along with the “existential evidence”.
No such expertise is required. Respondent’s misconception is that in paternity cases the HLA results are in real practice utilized and weighted, not “standing alone’, but along with the other evidence in the case.
HLA test results can be expressed in statistical form; the other evidence in a paternity case, as in most cases, is not expressed in statistical form. Respondent seems to think that because the HLA evidence is expressed as a quantifiable measure that the other evidence in the case (which respondent quaintly labels “existential”) must also be quantified, and an over-all quantifiable conclusion arrived at. This argument, at the very least, mislabels the process of weighing evidence.
Any trier of fact, in assessing evidence and arriving at a conclusion as to its weight, is applying probabilities. The point is that the probabilities tend to be implicit rather than explicit, and that the over-all result is expressed in a nonquantifiable judicial standard, such as “beyond a reasonable doubt” or “clear, convincing, and entirely satisfactory”. In the instant case, the court has weighed the HLA evidence along with all the other evidence in the case to arrive at a conclusion that respondent is the father of the subject child. Although the HLA evidence standing alone may only narrow the range of putative fathers, the HLA test combined with the other evidence in a case may pinpoint to a degree of virtual certainty who the father is. This case is an excellent illustration of this process.
*431The critical evidence in this case involves, inter alia, several elements: first, the HLA results; second, the fact that petitioner had sexual relations at or several months prior to the date consistent with conception (depending on whether petitioner’s or respondent’s version of the date of sexual relations is credited); and third, the credibility of petitioner and respondent as witnesses. The inference that the respondent is the father is not solely dependent upon the probability defined by the HLA test; rather, the inference depends upon the probabilities associated with the second and third elements. More specifically, the ultimate probability that the respondent is the father is a product of whether a respondent with a highly positive HLA test result (as in this case) and who admits to at a minimum having had sexual relations with the petitioner within a proximate period of months prior to conception and whose credibility as a witness is less than that of petitioner is in fact the father. Clearly, the ultimate probability that respondent is the father is increased by the probabilities associated with the second and third evidentiary elements.
Respondent suggests that statistical tests, such as Bayes’ Theorem, or statistical experts, are necessary to calculate the ultimate probability of paternity. Bayes’ Theorem is an example of a statistical test that is concerned with the relationship among conditional probabilities. Bayes’ Theorem, also known as Bayes’ Law, Bayes’ Formula, or the Rule of Bayes, is named after an English clergyman, Thomas Bayes, whose mathematical formula was first published in 1763.* (On the applications of Bayes’ Theorem, see Good, The Estimation of Probabilities: An Essay on Modern Bayesian Methods.) In statistical terms, conditional probabilities deal with the issue of the probability of a correct result given prior information about the situation. For example, the question of the probability (p) of x being the father of a particular child given a certain *432probability (p1) that x had prior intercourse with the mother at a particular time and/or given that x attained a certain HLA test result (p 2), is an exercise in conditional probability. (See Hayes, Statistics; Larson, Statistics: An Introduction.) Thus, there is a certain probability that a particular individual is the father of a given child, given that there is a highly positive HLA test result. As respondent notes, the HLA test does not calculate that probability precisely, but it does narrow the range. More complex applications of Bayes’ Theorem would be necessary to deal with a calculation based on multiple prior elements of information, i.e., not only HLA test results, but also evidence of the timing of intercourse, credibility of testimony, and so forth. (See Good, op. cit.)
However, the reason that statistical tests — including among others, Bayes’ Theorem — cannot be applied with precision to events such as the likelihood of paternity is that the underlying probabilities associated with all the evidentiary elements are not known. As one standard text on statistical probability aptly put it: “It [Bayes’ Theorem] is a useful formula, but its applicability is limited by the fact that in many cases the a priori probabilities involved in the formula are unknown.” (Alder & Roessler, Introduction to Probability and Statistics, p 68.) For example, it would have to be known, among other things, what the statistical association is between a positive HLA finding and the actuality of intercourse; the association between prior intercourse alone and paternity; the association between highly credible testimony and paternity, and so forth.
It is only because mathematical probabilities with respect to such evidentiary elements cannot be calculated, or are not available based on statistical experience, that ultimate paternity probabilities cannot be expressed with statistical precision. This does not mean that the judicial inference of paternity, based on a weighing of evidence, is untenable. The weighing of testimony to arrive at a judicial conclusion is, in essence, an exercise in the calculation of multiple conditional probabilities — estimating an ultimate probability, given prior information — without attaching mathematical probabilities to either the prior in*433formation or the ultimate conclusion. Thus, although the HLA test result itself can be expressed with some degree of statistical precision, it is clear that the fact that a respondent with a highly positive HLA test result also, as in the instant case, admitted to intercourse with the petitioner within a time frame proximate to conception, can only increase the ultimate probability that he is the father. When the element of positive credibility of the petitioner is added to the subjective equation, the odds become overwhelming that the respondent is the father. Although this ultimate probability cannot be expressed with mathematical precision, it can be appropriately expressed within the traditional judicial standard of constituting proof that is “clear, convincing, and entirely satisfactory”.
This standard of proof is all that one can and should require of the judicial process. It should be noted that, in theory, the probability of paternity in a particular case, and hence the quantum of proof correspondingly required, can never reach 100%. The reason for this is that it is impossible to prove with total certainty that, for example, a given respondent does not have an identical twin who conceivably could be the father of the child. The fact that no amount of judicial proof in a court hearing or trial can, by definition, ever reach a 100% degree of certainty may be distressing to some, but is even consistent with the field of modern physics where physicists, used to seeking and expressing their findings with mathematical precision, now accept the fact that even in the physical sciences, let alone the social sciences, no conclusion about reality can be expressed with absolute certainty, but only within degrees of probability. (See de Broglie, New Perspectives in Physics; Heisenberg, Physics and Philosophy: The Revolution in Modern Science.)
The clerk of the court is directed to enter an order of filiation, and the matter is further set down for a hearing on the issue of support on November 22, 1983, in Part 5.