Refer to the previous exercise. Suppose now that for a probability question, 100 answers are submitted, of which 50 are correct. Calculate the probabilities in Parts (a) and (b) of the previous exercise for the probability question.

Previous exercise

The National Public Radio show Car Talk used to have a feature called “The Puzzler.” Listeners were asked to send in answers to some puzzling questions—usually about cars but sometimes about probability (which, of course, must account for the incredible popularity of the program!).