Puzzler

Let's Make A Deal

You are lucky enough to have been selected as a contestant on a game show. There are three doors to choose from. One contains a car and the other two contain goats.

After you’ve chosen one but haven’t opened it, the host, who knows where everything is, reveals the location of a goat from behind one of the other two doors.

Should you stick with your original choice or switch, if you want the car?

Solution

You should switch. At the beginning, your choice starts out as a one in three chance of picking the car; the two doors with goats contain 2/3 of the chance. But, since the host showed you where one of the goats was, that 2/3 chance now rests solely with the third door (your choice retains its original 1/3 chance; you were more likely to pick a goat to begin with). The odds are better if you switch.