Physics & Math / Math

Take three cards, one painted blue on both sides, one red on both sides, and a third red on one side and blue on the other. Have your mark blindly draw a card and display one side, keeping the other side hidden. Let's suppose the side you see is blue. Now explain that he clearly didn't draw the double-red card, so the card must either be blue on both sides or red and blue; then wager even money that the other side is blue. Sounds like a fair bet, right? Wrong. The probability is in fact only one-third that the other side is red. The visible side could be the blue side of the red-blue card, or it could be either of the two blue sides of the double-blue card. In two out of these three equally likely scenarios, the double-blue card is the one in his hand, so the probability is twice as great that the other side is blue. Don't forget to send me a cut of your winnings!