Ten marbles labeled 1,2,...,10 are placed in a big jar and then stirred up. Zori, wearing a blindfold, pulls them out of the jar two at a time. Players are allowed to place bets as to whether the sum of the two marbles in a pair is 11. There are C(10,2)=45 different pairs and exactly 5 of these pairs sums to eleven. Suppose Zori draws out a pair; the results are observed; then she returns the two balls to the jar and all ten balls are stirred before the next sample is taken. Since the probability that the sum is an "11" is 5/45=1/9,, then it would be fair to pay one dollar to play the game if the payoff for an "11" is nine dollars. Similarly, the payoff for a wager of one hundred dollars should be nine hundred dollars. Now consider an alternative way to play the game. Now Zori draws out a pair; the results are observed; and the marbles are set aside. Next, she draws another pair from the remaining eight marbles, followed by a pair selected from the remaining six, etc. Finally, the fifth pair is just the pair that remains after the fourth pair