9.2 Exercise 26

Martha has the choice of two games.

1. Game 1Pay ten dollars for each “play.” If she wins, she receives $20, for a net gain of $10 on the play; otherwise, she loses her $10. The probability of a win is 1/2, so the game is “fair.”
2. Game 2Pay five dollars to play; receive $15 for a win. The probability of a win on any play is 1/3.

Martha has $100 to bet. She is trying to decide whether to play Game 1 ten times or Game 2 twenty times. Let $W 1$ and $W 2$ be the respective net winnings (payoff minus fee to play).

• Determine $P \left(W 2 \geq W 1\right)$.
• Compare the two games further by calculating $P \left(W 1 > 0\right)$ and $P \left(W 2 > 0\right)$

Which game seems preferable?