# Switch or Stick Question

A number of years ago, there was a popular television game show called Let's Make a Deal. The host Monty Hall, would randomly select contestants from the audience and, as the title suggests, he would make deals for prizes. 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 , 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 knows there is nothing behind that curtain C). He then offers you the 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 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?

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#### Solution Preview

1. Initially, the probability of car behind each of the three curtains was equally likely, hence

P(car Behind ...

#### Solution Summary

The Solution provides the best option for the probability question on Making a Deal.