In a game show, there is a game in which you have to order the value of three prizes in order of least expensive to most expensive. You have to get all three right in order to win.

The only problem is you have your spouse do all the shopping, so you only know that the first prize is between 500 and 2000, the second prize is between 1000 and 2500, and the third prize is between 1500 and 3000.

Which order should you put them in so that you have the highest probability of winning, and what is the probability that you will win using this arrangement?

(In reply to Solution provisions by Gamer)

The solutions actually consider a continuous range of prices and therefore probability zero that two are the same, which is the same as your statement that none have the same price.

When two prices are in the same band, most of these solutions assume one or the other is equally likely to be the larger. When three are in the same band, it's considered equally likely to be in any of the 6 possible orders, without consideration of the possibility that two are the same price. The same goes for the one of my solutions that does not make them equally likely, but still assumes that they are from a continuous distribution and therefore have zero likelihood of matching prices.

Posted by Charlie on 2003-10-20 11:41:08