July 2013 Brain Teaser Solution

Q: This is from the game show "Let's Make a Deal": 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?

A: This famous problem from the early 1990's was first discussed and debated in Marilyn Vos Savant's (the person with the highest IQ!) Parade column.  She received many letters saying she was wrong but most people agree once they read through this:

Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?

and this :  http://marilynvossavant.com/game-show-problem/