Problem

Suppose you’re on a game show, and you’re given the choice of three doors,


Behind one door is a car; behind the two others, goats. You pick a door, say No. 1, and the host of the show opens another door, say No. 3, which has a goat.


He then says to you, “Do you want to pick door No. 2?”.

Question: What would you do?

Is it to your advantage to switch your choice from door 1 to door 2? Is it to your advantage, in the long run, for a large number of game-tries, to switch to the other door?

Now whatever your answer is, I want you to check/prove your answer by a Monte Carlo simulation of this problem. Make a plot of your simulation for $\rm{ngames}=100000$ repeat of this game, that shows, in the long run, on average, what the probability of winning this game is if you switch your choice, and what is the probability of winning, if you do not switch to the other door.

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