Thursday, September 08, 2005
To switch or not to switch
The Monty Hall dilemma
You are probably familiar with the problem from the TV show ‘Lets make a deal’. Here is the problem. There are three doors and there is a car behind one of the doors and goats behind the other two doors. You don’t know which door the car is behind, but the game show host knows where it is. You get to pick a door and once you pick a door, the host will open a door with a goat behind from the remaining two doors (i.e. the doors you didn’t pick). Then you have two choices, either you stick with the door you originally picked or switch to the other door.
What would you do?
According to Marilyn Vos Savant, if you switch you have a higher probability to win. The reasoning being that 2 /3 times you will pick the wrong door and when the host opens a door with the goat, he has no choice but to pick the only other door with the goat behind. So 2/3 of the times if you switch you will get the car.
Not convinced yet? There is a computer simulation for this problem, which is fun to try out. Go to http://www.cut-the-knot.org/hall.shtml
So would you switch or stick?