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You are about to buy a car and the dealership is having a promotion in the form of a game. You are shown three boxes: one
contains a $1000 coupon and the other two contain a glass of water. You choose a box, but do not get to touch or open it. The dealer proceeds to open one of the two remaining boxes and pulls out a glass of water. He then gives you the option to switch to the box he did not open. Assuming you're not very, very thirsty, is it advantageous to switch your choice? Answer There are 2 possibilities after your fist selection: 1. The probability that you selected the correct box initially is 1/3. In this case you wouldn't want to switch. 2. The probability that you selected a wrong box initially is 2/3. In this case you would want to switch. As you can see, 2/3 of the time you would want to switch because you chose the wrong box initially. Therefore, the answer is yes, it is advantageous to switch your choice. back to math problem |