Financial Mathematics Text

Saturday, October 26, 2013

A Unique Solution to the Monty Hall Problem

The Monty Hall Problem is a counterintuitive result in statistics. The problem goes something like this.

Sketch of the Monty Hall Problem

Suppose there are three doors: A, B and C. Behind one of the doors is a big prize (a car, a huge pile of cash). Behind the other two doors are just some goats.

Now you make a selection of a door but the game is not over with yet. Suppose you pick door letter A. Now the game is not over with yet at this time. The host actually reveals one of the remaining doors, say door letter C, to have a goat.

Now the host gives you the option: stick with door A or switch to door B.

The counterintuitive result here is that you have a 2/3 shot at winning the big prize if you switch to door B. So if you want to win the prize you ought to change your answer to door B as that will give you better odds. (If you're not convinced, you can try out this simulator.)

The problem relies on the fact that people are not really good at dealing with conditional probabilities. 

An Alternative Solution to the Monty Hall Problem

So apparently there's another solution to the problem that I hadn't considered. The solution was proposed by Randall Munroe:

 I suppose I should throw in an idiom about old goats and new tricks.

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