80 of suspects tried for terrorism actually are guilty Dont

80% of suspects tried for terrorism actually are guilty. (Don’t worry about how we know this, just take it as a fact for the sake of this problem.) Also, the probability that a person suspected of terrorism will confess after prolonged questioning is 40% if the suspect is innocent, and 15% if the suspect is guilty.

A suspect, Josef K., is being tried for terrorism. If he confessed after prolonged questioning, what is the probability that he is actually guilty? And how can you explain this puzzling result? (First of all, you may need to explain why it is puzzling. Then explain why it really makes sense even though it seems to be puzzling.)

Note: You may use contingency tables or any other method to find the probability in this problem. First, set up notation for the various events involved: make sure that you state clearly what event each letter stands for, and translate the given probabilities into that notation. Your grade will be based partly on how well you set up the notation.

Solution