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.
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