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The Monty Hall dilemma



What is it?


The Monty Hall dilemma gets its name from the host of an old American quiz show called "Let's make a deal".

It has some important concepts to do with probability and shows us that things are not always as they seem
It also teaches us to be very careful when making assumptions, and those of you who have encountered the problem before would do well to take great care when reading the problem on this page.



Yes..but what's the problem?



The problem is as follows:

You are on a gameshow and have reached the final game.
In front of you are three doors, labelled, imaginatively, A, B and (wait for it) C.

The host informs you that you must choose a door to open. Behind two of the doors is a goat (Two goats, one each door) and behind the other is a sports car.
You get to keep the prize behind the door that you open.

You consider carefully, and finally the audience baying of 'choose A' 'no choose C' and 'BBBBB' subsides and you decide to plump for door B.

The host now does you a favour.
He walks up to door A and opens it, revealing a goat.

He now offers you the option to change your original guess.

The question is, does changing your mind work to your advantage?


Have a think then read solution
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