Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

Source: http://en.wikipedia.org/wiki/Monty_Hall_problem

Solution:
If you switch, you get the car with probability 2/3. So switching is always a good choice. Refer this MIT video lecture for great explanation. Refer online editable Monty hall simulation to play with how things change with multiple doors, prizes etc.

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