Political prisoners Mathew, Mark, and Luke are told that two of the three are to be executed. Matthew takes the jailer aside and says, "We both know that at least one of the others, Mark or Luke, will be executed; if you know, tell me the name of one who will be executed." After mulling this request over, the jailer can see no harm in revealing one name and tells Matthew that Mark will be executed. Thereupon Matthew rejoices because the probability of his execution has just decreased from 2/3 to 1/2. Is his elation justified?
Yes, his thought is correct -- although there's nothing to be cheerful.
This is a conditional probability question.
The unconditional probability of Matthew to be executed is obviously 2/3,
and the ...
The following works through a conditional probability exercise regarding a prisoners likelihood of being executed. Formulas and explanations of steps are provided.