[montyhallstuff]

Just in case....

A sample space is the set of all possible outcomes of a random experiment. An event is a subset of a sample space.

Let S be the finite sample space with equally likely outcomes in it. Let E be an event. Then the probability of E is the number of outcomes in E over the total number of outcomes in S.

Now consider 52 cards in a deck. The sample space of outcomes here are the 52 cards. What is the event that the chosen card is a black face card? E = {J-club,Q-club,K-club,J-spade,Q-spade,K-spade}. What is the probability that the chosen card is a black face card? 6/52 by the formula above.

Monty Hall problem can be solved by using the above as a guide.

Sample space here : {switch, switch, stay-with-your-original-choice}. By the formula above, the probability of switching is 2/3 and the probability of staying put is 1/3.

If you're doubting the formula, I can provide you with a proof.

[retsibsi]

As I mentioned in another comment, it's important to note that Monty Hall is guaranteed to open a door with a goat behind it (a losing door). If he chose randomly and just happened to reveal a goat, the answer would be different.

[disgruntledphd2]

Indeed. This is the major reason I don't like the Monty Hall problem. When using stats and probability (at least in science), the universe is not your adversary.