Probabilities and Courtroom Drama
In 1964 a Los Angeles blond woman with a ponytail snatched a purse from another woman. The thief was spotted entering a yellow car driven by a black man with a beard and a mustache. The police eventually found a blond woman with a ponytail who regularly associated with a bearded and mustachioed black man who owned a yellow car, but there was no hard evidence linking them to the crime. In court, the prosecutor argued that the probability was so low that such a couple existed that the police must have found the actual culprits. The prosecutor assigned the following probabilities to the characteristics in question:
yellow car: 1 in 10 or 1/10
man with a mustache: 1/4
woman with ponytail: 1/10
woman with blond hair: 1/3
black man with beard: 1/10
interracial couple in a car: 1/1000
The prosecutor argued that the characteristics were independent, so the probability that a randomly selected couple would have them all would be:
(1 x 10) x (1 x 4) x (1 x 10) x (1 x 3) x (1 x 10) x (1 x 1000) = 1 in 12,000,000
This, he argued, was a probability so low that the couple must be guilty. The jury agreed and convicted them.” (extract from: Innumeracy-Mathematical Illiteracy and its Consequences)
BUT, the case was appealed to the California Supreme Court. What do you think the outcome was? (more in another post soon)