The Monty Hall problem is a probability puzzle credited to statistician Steve Selvin, made famous by game show host Monty Hall. Steve published the puzzle and the solution in The American Statistician, a scientific journal in 1975.
Suppose that there are three doors. There is a car behind one of the doors, and goats behind the other two doors. You, as a contestant, do not know which door holds which. You are asked to pick a door. Let's say you pick door 1. The host, who knows what's behind each of the doors, opens one of the other doors, say door 3, to reveal a goat. Now you are given the option of switching your choice from door 1 to door 2. Does switching your choice increase your probability of winning the car?
The solution provided by Steve in 1975 and later in 1990 by Marilyn vos Savant generated a lot of controversy and made the puzzle famous throughout the world. A number of articles and papers were published on the puzzle. Mathematicians and PhDs provided formal proofs and computer simulations in support of the solution.
Consider the problem carefully. Your first choice, door 1, gives you a 1/3rd chance of winning the car. If you consider the other two doors as a set (door 2 and door 3), the chances of finding the car behind one of those doors is 2/3rd. Now the host opens one of those doors to reveal the goat. So the other door still retains the 2/3rd probability while your original choice has just a 1/3rd probability. So it is to your advantage to switch to door 2.