Question: Martha has the choice of two games.
Game 1: Pay 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."
Game 2: Pay 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 W1 and W2 be the respective net winnings (payoff minus fee to play).
- Determine P (W2 ≥ W1).
- Compare the two games further by calculating P (W1 > 0) and P (W2 > 0)
- Which game seems preferable?