9. In-class activity The Monty Hall problem is based on the old television game
ID: 3314235 • Letter: 9
Question
9. In-class activity The Monty Hall problem is based on the old television game show Let's Make a Deal, hosted by Monty Hall. Suppose you are a contestant who has selected one of three doors after being told that two of them conceal nothing, but that a new red Corvette is behind one of the three. Next, the host opens one of the doors you didn't select and shows that there is nothing behind it. He then offers you the choice of sticking with your first se- lection or switching to the other unopened door. Should you stick with your first choice or should you switch? Divide into groups of two and simulate this game to determine whether you should stick or switch. (According to Chance magazine, business schools at such institu- tions as Harvard and Stanford use this problem to help students deal with decision making.)Explanation / Answer
At the beginning, before the contestant chooses a door, the probability of each door containing the car = 1/3
Let's say the contestant chooses door x.
The probability of both the other doors contaning the car = 1/3 + 1/3 = 2/3
The host purposefully opens the door which doesn't have a car. So now, the probability of the other unopened door (other than X) containing the car = 2/3
Hence, it would be prudent to switch the door.
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