Three doors

January 1998

This issue's puzzle is based on a well-known problem in probability.

Red door
Green door
Blue door

A game show host hides a prize behind one of three doors. The contestant has to guess which door hides the prize. The rules of the game are as follows.

Firstly, the contestant chooses a door and tells the host this is the one she thinks the prize is behind. The host must then open one of the other doors. Of course, the host does not want to reveal the whereabouts of the prize so he always opens a losing door.

The host then asks the contestant if she would like to stick with the door she originally chose or switch to the other unopened one.

Should she switch doors?

We will publish the best explanation in the next issue, along with the answer to the problem itself.



No, she should stay with her first thoughts on the door that she picked, because now she has a even chance of winning a prize.

Switch doors to get a 67% chance of winning the prize. The door you pick 1st has a 67% chance of NOT containing the prize, forcing the host to open the other non-prize door, leaving the door the host didn't open with a 67% chance of hiding the prize.