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From Mathsoc wiki

Does anyone believe santa?

I believe in Santa.

Does anyone believe in the Monty Hall problem?

please note that any similarity to a certain stats assignment is totally incidental and certainly not evidence of an equivalence relationship.

Saying that; Three doors are labelled A,B, and C. Behind one door is a massive book, full of equations and theorems.Actually there is a cheque for lots of money. Behind the other doors is a goat/fionnan. You are asked to pick a door. After your choice the presenter(whom knows which door contains money/Fionnans) opens one door to reveal a goat.

You are now given the option of switching to the remaining door. Should you switch? Why?

Yes you should always switch. Let us say that the money is fixed at A.

We have three choices.

1) we pick A.

  The host reveals door B/C to hide a goat.
  We switch to B and we lose(unless you like goats).

2) We pick B.

  The host reveals C to contain a goat.
  We switch to A. 
  We win lots of money(which can buy many goats).

3) We pick C

  The host reveals B to contain a goat.
  We switch to A
  again we win lots of money.

  Therefore by switching we will win 2/3 of the time.

For further examples of the Monty Hall problem and different solutions( and infomation about the controversy surrounding the problem) see Simon Singh's Fermat's Last Theorem, Wikipedia, Wolfram's Mathworld etc.