Question: Let’s Make a Deal

A number of years ago, there was a popular television game show called Let’s Make a Deal. The host, Monty Hall, could randomly select contestants from the audience and, as the title suggests, he would make deals for prizes. The contestants would be given relatively modest prizes and would then be offered the opportunity to risk those prizes to win better ones.

Suppose that you are a contestant on this show. Monty has just given you a free trip touring toxic waste sites around the country. He now offers you a trade: Give up the trip in exchange for a gamble. On the stage are three curtains, A, B, and C. Behind one of them is a brand new car worth $20,000. Behind the other two curtains, the stage is empty. You decide to gamble and select curtain A. In an attempt to make things more interesting, Monty then exposes an empty stage by opening curtain C ). He then offers you a free trip again if you quit now or, if you like, propose another deal (i.e., you can keep your choice of curtain A or perhaps switch to curtain B). What do you do?

To help you answer that question, try first answering these questions.

1. Before Monty shows you what’s behind curtain C, what is the probability that the car is behind curtain A? What is the probability that the car is behind curtain B?

2. After Monty shows you what’s behind curtain C, what is the probability that the car is behind curtain A? What is the probability that the car is behind curtain B?