I heard an interesting problem yesterday evening:

“A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. ‘First you point toward a door,’ he says. ‘Then I’ll open one of the other doors to reveal a goat. After I’ve shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door.’ You begin by pointing to door number 1. The host shows you that door number 3 has a goat.” (Mueser and Granberg 1999)

Should you switch doors? What is the probabilty of winning if you do switch? What is it if you don’t switch? Does the switch matter?

(solution)