Monty Hall Problem
The Monty Hall Problem is a probability problem based on the TV game show called Let’s Make a Deal from the 1960s hosted by Monty Hall (1921-2017).
You’re on a game show, and you are given a choice of three doors. Behind one door is a car while behind each of the other two is a goat. You choose one door, say, number 1, and the host – who knows what’s behind the doors – opens another door, say number 3, which has a goat behind it. To win the car, you can stick to the door you first picked or choose the other one, number 2 in this example.
Question: To win the car, do you stick to your first pick, or do you switch?
Use your knowledge of probability to find the probability of winning the car if you
a) stick to your first choice b) switch
Spend about 20-30 minutes figuring out the solution. Draw three doors labeled 1, 2, 3, and ask yourself why this is a probability problem. Use your understanding of the basic definition of probability to solve it. Take this as a challenge and really test yourself.
If you are struggling, you are in good company because the Monty Hall problem stumped some of the leading mathematicians of the 20th-century when it first appeared. After you have given it your best shot, you can look at one or both these videos to gain insight into the problem.
https://www.khanacademy.org/math/precalculus/prob-comb/dependent-events-precalc/v/monty-hall-problem
What is expected from you
As clearly as possible and in your own words,
explain what the two probabilities are (don’t switch/switch)
to win the car. Clearly explain the solution as you
understand it, using your own words. (12-15 sentences
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