You look at a carnival game. The person running it says, "Just reach your hand into this bag. There are 9 yellow balls and 1 red ball in the bag. You get 4 chances to pull out the red ball. (You have to put the ball you drew back before you draw another ball.) You only have to pay one dollar to play, and you get 3 dollars if you pull out the red ball!"

Assuming the person running the game is telling the truth, and the balls only differ in color, would you expect to make a net profit or a net loss on this game?

(In reply to Solution by Senthil Kumar)

Senthil,

You are misunderstanding the problem. When you pay $1, you get to try 4 times to pull out the red ball. But if you pull it out on the first try, you get $3 and the game is over. You don't get 3 more tries, you are done.

You analysis is equivalent to saying you pay 25 cents for each chance to pull out the red ball, and each time you pull it out you win $3. This is not the same thing. In this case, indeed, your expected winnings would be 5 cents per draw. But in the game as stated (1 game = 4 draws, you win $3 if any of the draws gives you a red ball), the expected winnings are about 3 cents per game, as fwaff showed. This is much lower than your 20 cents per four draws.

Posted by Brian Wainscott on 2003-09-18 19:00:20