You are one of 20 logicians worldwide to receive this letter. You don't know each other, but you all think alike. An address is given, and you are told that if a letter is received from one and only one of you, all 20 will equally split a large sum of money. If no letters are received, or more than one, no prize.

What would you to for a chance of winning the prize? What could you do in order to maximise the probability of winning?

You could think of it as the probability of a particular person x being the only one to send in the letter times the number of people. The odds that x sends a letter is 1/20. The odds that each of the other 19 people don't send a letter is (19/20)^19. Since x can actually be any one of 20 people, that probability is multiplied by 20. That gives (1/20) x (19/20)^19 x 20 = ~0.377 = ~37.7%.

Posted by friedlinguini on 2003-01-02 11:39:44