A famous problem in probability comes from the game show “Let’sMake a Deal.” In it, a contestant is shown threedoors. Behind one door is a new car, and behind theother doors, there is nothing. The contestant is askedto pick one of the three doors. The host then opens upone of the two that was not chosen which always reveals that thereis nothing behind that opened door. The contestant isthen asked if he or she would like to change their chosen door tothe other unopened one.
A) Should he/she? Explain why or why not. (Expressesopinion about whether the contestant should change his/herdecision, and supports that opinion through sound application ofthe concepts of probability)
B) Can you think of another example where someone's intuitionabout probability may lead them down the wrong path?
