Recreational Math

Just For Fun

What is the Monty Hall Problem?

Let’s Make a Deal, a once-popular television game show with host Monty Hall (who was the master of ceremonies from 1963 to 1986), is the origin of the Monty Hall Problem. The same type of problem is also represented in a card game called “three-card monte.”

The Monty Hall Problem is similar to the show. A contestant is given a choice of three doors. Behind one is a car; behind the other two there is nothing. The host asks the contestant to pick a door. After the pick, the host opens one of the unpicked doors—one the host knows is empty. The host then suggests a switch. The big question, and the problem, becomes does the contestant switch his or her choice or keep the originally chosen door?

The mathematical, statistical answer is yes, switch the doors. Why? Because the original probability that the contestant picked the correct door does not change—it is still 1/3. But if the contestant does switch, the probability becomes 2/3. Most people believe that once one of the doors is eliminated, the probability between the remaining doors becomes 50-50, but it does not.


This astronaut on the Moon weighs only 17 percent of what he would weigh if he were standing on the Earth.


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