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You are participating in a TV game. You have reached a stage where you can select one box out of three knowing that only one contains a cash prize and the others contain nothing. The TV host knows which of the boxes contains the prize. Having made your choice, the host decides to reveal the content of one of the two boxes you haven't selected which he knows is empty. He then offers you the possibility to change your selection. Should you switch or stick to your choice? does it matter?

Answer: It does matter! - you should switch!

1)The probability of getting it wrong first time is 2/3. The host then has no other choice then to reveal the content of the single unselected empty box. In this case switching would win you the prize.

2)In the less likely situation that you do get it right first time, the TV host will have the choice between revealing the content of any of the two unselected boxes. In this case switching would make you lose.

Since case 1 is twice as likely as case 2, the probability of finding the prize having done a switch is 2/3.

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