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
re: Solution by Bryan)
Huh? I'm not sure what you mean by "Statistically speaking, winning and losing comes in streaks." The first rule of statistics is that each trial is completely independent from what came before. Now, since the advantage over the house in this case isn't huge, you are right that for any one person coming to the stall with just a few bucks, they may well lose, but the chance of them winning is greater. Put it another way: Over the course of the day the house will have lost money. Therefore on average the players must have won money, even if each one only came with a couple of bucks.

Posted by Sam
on 20030918 11:42:21 