Thứ Bảy, 21 tháng 3, 2009

Probability and the law

Problem Solving – a Statistician’s Guide – 2nd ed by Chris Chatfield
Chapman & Hall 1988, 1995

Exercise G1 – Probability and the law
(p. 215)
In a celebrated criminal case in California (People versus Collins, 1968), a black male and a white female were found guilty of robbery, partly on the basis of a probability argument. Eyewitnesses testified that the robbery had been committed by a couple consisting of a black man with a beard and a moustache, and a white woman with blond hair in a ponytail. They were seen driving a car which was partly yellow. A couple, who matches these descriptions, were later arrested. In court they denied the offence and could not otherwise be positively identified.

A mathematics lecturer gave evidence that the six main characteristics had probabilities as follows:

Negro man with beard 1/10
Man with moustache 1/4
Girl with pony tail 1/10
Girl with blond hair 1/3
Partly yellow car 1/10
Inter-racial couple in car 1/1000

The witness then testified that the product rule of probability could be used to multiply these probabilities together to give a probability of 1/12 000 000 that a couple chosen at random would have all these characteristics. The prosecutor asked the jury to infer that there is only one chance in 12 million of the defendants’ innocence, and the couple were subsequently convicted.

Comment on the above probability argument.

(Please come back next week for the solution!)

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