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Probability theory was used in a famous court

case: People v. Collins. 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.

{\rm man with mustache}

1/4 \cr{\rm girl with blond hair}

1/3 \cr{\rm girl with ponytail}

1/10 \cr{\rm black man with beard}

1/10 \cr{\rm interracial couple in a car}

1/1000 \cr{\rm partly yellow car}

1/10 \cr

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 \ref{sec 5.1}..)

Notes