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?

There are 10 balls in the bag. 9 are yellow and 1 is red.  Thus, one has 9/10 of a chance of pulling out the yellow ball and 1/10 of a chance of pulling out the red ball.  Your chances of pullling out a red in exactly one of the four tries is 1/10+(9/10*1/10)+(9/10*9/10*1/10)+(9/10*9/10*9/10*1/10)= 3439/10000 or a little over 1/3 of the time.  Because of the this one would expect to make a slight net profit on the game.  This is because, one will pay about $3 before they are able to pull the red ball out of the bag (thus accumlating $3).  However, if the process is done multiple times, then one will come out slightly ahead (because the probability is a little over 1/3 of the time).

Posted by logischer Verstand on 2004-04-13 21:59:21