The Monty Hall Problem
I first saw this problem when I was watching the movie ‘ 21’ . The re is a short classroom scene where Professor Micky Rosa tests Ben Campbell with what sounds like a simple probability puzzle. This is their conversation. Professor: Ben, suppose you're on a game show and you are given a chance to choose from three different doors. Now behind one of the doors is a new car and behind the other two – goats. Which door would you choose? Ben: Door number 1. Professor: Ben chooses door number 1! The game show host, who by the way knows what's behind all the other doors, decides to open another door. Let's say he chooses door number 3… behind which sits a goat. Now, Ben – the game show host comes up to you and says, “Ben, do you want to stay with door number 1 or go with door number 2”? Now is it in your interest to switch your choice? Ben: Yeah. Professor: Well, wait – remember the host knows where the car is so how do you know he's not play...