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 Bart freeman)

No, that's not correct. The chance of failure is 90% in the first try, but not for the whole game.
The probability of an event is calculated by the summation of ALL possibilities that lead to a success. Draw a tree graph and you will see four different branches.
Your method would only account for the first draw, in other words the first branch of that tree.

Posted by abc on 2003-09-19 11:03:07