Probability theory was used in a famous court case: People v. Collins.10 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.

The prosecution then argued that the probability that all of these character- istics are met by a randomly chosen couple is the product of the probabilities or 1/12,000,000, which is very small. He claimed this was proof beyond a rea- sonable doubt that the defendants were guilty. The jury agreed and handed down a verdict of guilty of second-degree robbery.

Table: Collins case probabilities.

If you were the lawyer for the Collins couple how would you have countered the above argument?