### Home > PC3 > Chapter 12 > Lesson 12.3.2 > Problem12-145

12-145.

Jack is designing a game for the school fundraiser. Players will be paying $5$ for each time they play the game. There will be three prizes. The smallest prize has a value of $5.50$; the next prize has a value of $8$. Jack has not yet determined the value of the largest prize. The probability of winning the smallest prize is $0.15$, the probability of winning the second prize is $0.05$, and the probability of winning the largest prize is $0.01$. The probability of not winning any prize is $0.79$. If the school wants earn an expected value of $1$ per game played, what should Jack choose as the value of the largest prize?

If the school wants to earn \$1 per game played, then the expected value for the player is $−1$.

$0.15(0.50) + 0.05(3.00) + 0.05(x − 5.00) + 0.79(−5.00) = −1$