Day #26 Advent Post: Thank you all!

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How to Win a Sportscar Using Probability

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Some of you may have heard about The Monty Hall problem. It originates from the American television game show Let's Make a Deal and named after its original host, Monty Hall. It goes as follows: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sportscar. Behind the others there are only goats. You pick a door, say No. $1$, and the host, who knows what's behind the doors, opens another door, say No. $3$, which has a goat. He then says to you, "Do you want to pick door No. $2$?" Is it to your advantage to switch your choice? At first glance, this problem seems simple. But it’s one of those puzzles where our intuition completely misleads us. It’s a perfect example of how probability defies common sense. The original question became famous as a question from reader Craig F. Whitaker's letter quoted in, and solved by, Marilyn vos Savant in the Ask Marilyn column in Parade magazine in $1990$. Before we...
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