Calculating Probability

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The Monty Hall problem is loved by statisticians around the world [1]. You might be familiar with this puzzle, in which a game show host offers a contestant a choice of three doors – behind one door is a prize, but the other two doors only reveal goats. After the contestant chooses a door, the TV host opens a different door, revealing a goat, and asks the candidate to reconsider (Figure 1). Who would have thought that probabilities in a static television studio could change so dramatically just because the host opens a door without a prize?

Figure 1: Hoping to win the car, the contestant chooses door 1. The host, who knows which door leads to the car, then opens door 3, revealing a goat. He offers the contestant the option of picking another door. Does it make sense for the contestant to change their mind and go for door 2? (Source: Wikipedia)

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