Question 8.44

image 13. In Spotlight 8.1 (page 345), we noted that a question posed to Blaise Pascal in 1654 by an amateur mathematician launched the formal study of probability. Here’s a simplified version of this “Problem of Points.” Suppose two players are playing a coin flip game where “heads” earns Player A one point and “tails” earns Player B one point. The winner is the first player to reach a total of four points. The game is interrupted with Player A ahead by a score of 3 to 2. Based on the sample space of possible ways that the game can be finished, what would be a fair division of the jackpot money between Players A and B?

13.

If the next flip is heads, Player A wins; if tails, the two players will be tied and will have to flip the coin again. Thus, the probability of Player A winning is . The probability of Player B winning is . To be fair, Player A should receive of the jackpot money and Player B should receive of the jackpot money.