This monte think is starting to get to me [img]/images/graemlins/smile.gif[/img]

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The way that I think it is best explained is by looking at all the possible outcomes.

Assume the prize is behind door 3
If you never switch the outcomes are:
You pick door 1, the host shows you door 2, you stay with door 1. Outcome: lose
You pick door 2, the host shows you door 1, you stay with door 2. Outcome: lose
You pick door 3, the host shows you door 1 or 2, you stay with door 3. Outcome: win & W

If you always switch the outcomes are:
You pick door 1, the host shows you door 2, you switch to door 3. Outcome: win
You pick door 2, the host shows you door 1, you switch to door 3. Outcome: win & win (!)
You pick door 3, the host shows you door 1 or 2, you switch to door 1 or 2. Outcome: lose and lose (!).

Therefore by not switching you win 2/4 times. By switiching you win 2/4.




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FYP