Let’s Make a Deal. Monty Hall was the host of the once-popular television game show Let’s Make a Deal. At certain times during the show, a contestant was allowed to choose one of three identical doors...

Let’s Make a Deal. Monty Hall was the host of the once-popular television game show Let’s Make a Deal. At certain times during the show, a contestant was allowed to choose one of three identical doors A, B, and C, behind only one of which was a valuable prize (a new car). After the contestant picked a door (say, door A), Monty opened another door and showed the contestant that there was no prize behind that door. (Monty knew where the prize was and always chose a door where there was no prize.) He then asked the contestant whether he wanted to stick with his choice of door or switch to the remaining unopened door. Should the contestant have switched doors? Did it matter?