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People v. Collins, 68 Cal.2d 319 (1968)


Probative weight of evidence - mathematical probability


A woman was robbed on the street without seeing the perpetrator approach. After she was pushed down she was able to look up in time to see a woman fleeing the scene and a few other details. Mathematical probability was introduced as evidence in an attempt to prove who the perpetrators were.

In a robbery prosecution, the prosecutor misused mathematical probability statistics in an attempt to show that defendants were the robbers where there was no evidence relating to any of the six individual probability factors used by the prosecutor and ascribed to the distinct characteristics of defendants, and where no proof was presented that the characteristics selected were mutually independent, even though the mathematical

expert witness acknowledged that such condition was essential to proper application of the statistical probability rules that he used in his testimony.


Whether mathematical probability can be used to establish guilt. Whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case.


That on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial.


In a criminal case, it was prejudicial error to allow the prosecution to offer, through an expert, a formula in statistical probability, logically irrelevant and evidentially inadequate, from which the jurors were invited to infer that the odds against defendants' innocence were one in 12,000,000, where the circumstantial nature of the evidence and length of the jury deliberation showed that the case was a close one, and where, under the circumstances, the "trial by mathematics," with which the jurors were not technically equipped to cope, so distorted their role and so disadvantaged defense counsel as to constitute in itself a miscarriage of justice.


The prosecution's misuse of mathematical probability statistics was prejudicial where the testimony lacked an adequate foundation in evidence and in statistical theory, where it was used to distract the jury and encourage them to rely on a logically irrelevant expert demonstration, where it foreclosed the possibility of an effective defense by an attorney unschooled in mathematical refinements, and where it placed the jurors and defense

counsel at a disadvantage in sifting relevant fact from inapplicable theory.


FN10 Although the prosecutor insisted that the factors he used were only for illustrative purposes-to demonstrate how the probability of the occurrence of mutually independent factors affected the probability that they would occur together-he nevertheless attempted to use factors which he personally related to the distinctive characteristics of defendants. In his argument to the jury he invited the jurors to apply their own factors, and asked defense counsel to suggest what the latter would deem as reasonable. The prosecutor himself proposed the individual probabilities set out in the table below.

Although the transcript of the examination of the mathematics instructor and the information volunteered by the prosecutor at that time create some uncertainty as to precisely which of the characteristics the prosecutor assigned to the individual probabilities, he restated in his argument to the jury that they should be as follows:

Characteristic Individual Probability

A. Partly yellow automobile 1/10

B. Man with mustache 1/4

C. Girl with ponytail 1/10

D. Girl with blond hair 1/3

E. Negro man with beard 1/10

F. Interracial couple in car 1/1000

In his brief on appeal defendant agrees that the foregoing appeared on a table presented in the trial court.

Applying the product rule to his own factors the prosecutor arrived at a probability that there was but one chance in 12 million that any couple possessed the distinctive characteristics of the defendants. Accordingly, under this theory, it was to be inferred that there could be but one chance in 12 million that defendants were innocent and that another equally distinctive couple actually committed the robbery. Expanding on what he had thus purported to suggest as a hypothesis, the *326