BBy Bot
Jun 09'24

Exercise

Probability theory was used in a famous court case: People v. Collins.[Notes 1] In this case a purse was snatched from an elderly person in a Los Angeles suburb. A couple seen running from the scene were described as a black man with a beard and a mustache and a blond girl with hair in a ponytail. Witnesses said they drove off in a partly yellow car. Malcolm and Janet Collins were arrested. He was black and though clean shaven when arrested had evidence of recently having had a beard and a mustache. She was blond and usually wore her hair in a ponytail. They drove a partly yellow Lincoln. The prosecution called a professor of mathematics as a witness who suggested that a conservative set of probabilities for the characteristics noted by the witnesses would be as shown in Table.

Collins case probabilities.
man with mustache 1/4
girl with blond hair 1/3
girl with ponytail 1/10
black man with beard 1/10
interracial couple in a car 1/1000
partly yellow car 1/10

The prosecution then argued that the probability that all of these characteristics are met by a randomly chosen couple is the product of the probabilities or 1/12,00,00, which is very small. He claimed this was proof beyond a reasonable doubt that the defendants were guilty. The jury agreed and handed down a verdict of guilty of second-degree robbery. If you were the lawyer for the Collins couple how would you have countered the above argument? (The appeal of this case is discussed in Exercise).

Notes

  1. M. W. Gray, “Statistics and the Law,” Mathematics Magazine, vol. 56 (1983), pp. 67--81.