Prime Suspect

Question

One of these four people has committed a crime. Two detectives are working on the case. One says there’s a 2 in 3 chance that the culprit wears glasses. The other says the culprit was wearing a hat. Who is your prime suspect?

Courtesy of Alex Bellos. Think Twice

People often think the answer is John, as he has both glasses and a hat. If there is a 2 in 3 chance that the murderer wears glasses then it is 66.6% likely that it is John, Jane or Jeremy. In other words, the likelihood of each of these suspects being the murderer is 22.2%, and the chance that Jenny is the murderer is 33.3%. If the prime suspect definitely wears a hat, it must be either John or Jenny and we have already seen that Jenny is the more likely of those two, therefore she is the prime suspect.

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