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 then would be offered the opportunity to risk that prize to win better ones.
Suppose you are a contestant on this show. Monty has just given you a free trip worth $500 to a locale that is of little interest to you. 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 $45,000. Behind the other two curtains, the stage is empty.
You decide to gamble and give up the trip. (The trip is no longer an option for you.) You must now select one of the curtains. Suppose you select Curtain A.
In an attempt to make things more interesting, Monty then exposes an empty stage by opening Curtain C (he knows that there is nothing behind Curtain C). He then asks you if you want to keep Curtain A, or switch to Curtain B.
What would you do? What is your best strategy to win the car after curtain C is opened?
Hint: Questions to consider are: What is the probability of winning and the probability of losing the car prior to opening Curtain C? What is the probability of winning and the probability of losing the car after opening Curtain C?