Math Puzzle No. 2: The Monty Hall Problem
COME ON DOWWWWNNNN!!!!!! You’ve been chosen to be a contestant on Let’s Make a Deal! You’re now standing in front of three doors -- behind one of these doors is a car, and behind each of the other two is a goat. Monty, the host, says, “Pick a door! If it has the car behind it, you’ll drive it home today!” You choose door #1, and feel really good about your choice. The host then opens door #3, which has a goat behind it, and asks “Do you want to switch doors?” Question: What is the probability that you will win the car now that you know there was a goat behind door #3? Should you switch? Assumptions: Before the show, the car was equally likely to be placed behind any of the three doors. Once you make your selection of door #1, Monty will choose to reveal what is behind one of the other two doors, but will definitely not show you where the car is. Update: 11/19/20: read below for the solution.