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?

Another tricky one from Gamer !! If he had asked "Assuming the person running the game is telling the truth, and the balls only differ in color, WOULD you make a net profit or a net loss on this game?" then the correct answer is that you would make a slight profit. It stands to reason. You would expect to pull out a red ball every 10th time. And since it only costs a dollar to try 4 times, you would only spend 5 dollars to try 20 times. And in 20 attempts, you would probably draw the red ball twice - you would win 6 dollars. BUT....that is NOT the question that the devious and subtle Gamer asked !! He asked "would you EXPECT to make a net profit or a net loss on this game?" The answer is that you would EXPECT (wrongly) to make a net loss, since the ever fallible human intuition invariably comes to the wrong conclusion about this, and thinks that you would lose money. Why do you think Gamer deliberately placed this game in a CARNIVAL ????? As I said, IT TOOK REAL BALLS TO PUT THIS RIDDLE OUT HERE !!!!!!!!!!!!

Edited on September 19, 2003, 3:49 am

Edited on September 19, 2003, 3:49 am

Edited on September 19, 2003, 3:51 am

Edited on September 19, 2003, 3:57 am
Edited on September 19, 2003, 4:02 am

Posted by Dan on 2003-09-19 03:47:41