In an actual case,* probability was used to convict a couple of mugging an elderly woman. Shortly after the mugging, a young, white woman with blonde hair worn in a ponytail was seen running from the scene of the crime and entering a yellow car that was driven away by a black man with a beard. A couple matching this description was arrested for the crime. A prosecuting attorney argued that the couple arrested had to be the couple at the scene of the crime because the probability of a second couple matching the description was very small. He estimated the probabilities of six events as follows:
Probability of black-white couple: 1/1000
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Probability of black man: 1/3
Probability of bearded man: 1/10
Probability of blonde woman: 1/4
Probability of hair in ponytail: 1/10
Probability of yellow car: 1/10
He multiplied these probabilities and concluded that the probability that another couple would have these characteristics is 1y12,000,000. On the basis of this circumstantial evidence, the couple was convicted and sent to prison. The conviction was overturned by the state supreme court because the prosecutor made an incorrect assumption. What error do you think he made?