You are on a game show. There are 3 doors A,B,C. Behind two of the doors are goats. Behind one door is the keys to the star prize a dream home. You are given a free choice. After choosing a door. The host (who knows where the keys are) opens one of the other doors to reveal a goat. He now asks whether you want to stick with your original choice or swap to the other closed door. What do you do? Swap or stick? Or does it not matter?
Swapping is right. It becomes more obvious if you start off with 100 doors, pick one, and then the host opens 98 doors showing 98 goats, leaving just two doors - the one you picked and another. The chance of you picking the right door first time was 99:1 so 99 time out of 100 the goat will be behind the other door, so 99% of the time it is right to swap.