A group of crazy bank robbers try to crack a safe, even though they don't have a clue what the code is. The code has 5 numbers in, and the numbers on the dial range from 1 to 60. If they crack the safe, they get £100 billion.(That's a British billion - a million million). If they get the code wrong, they get caught and fined £1 million.

Assuming the bank robbers don't enter the same code twice, if they keep trying and re-trying until they crack the safe, are they more likely to have lost or gained money? If so, how much would they probably gain/lose?

Assuming the robbers know whether to start by going clockwise or counterclockwise, and that any given number can appear any number of times, and in succession, there are 60^5 possible combinations. That's 777.6 million combinations. On average, then, the robbers would have to try 388.8 million times, thus averaging 388.8 British billion pounds in order to get 100 British billion pounds, or an expected loss of 288.8 billion pounds.

Posted by Charlie on 2003-08-11 09:43:59