Expected Value
Mr. Random is a ninth grade math teacher who likes to play games of chance with his students. On the first day of school, he gives them a choice of two games which can be played for extra credit points.
Game 1: A wheel has three numbers on it: 0, 2 and 4. When it is spun there is a 40% chance that the wheel lands on 0, a 10% chance the wheel lands on 2, and a 50% chance the wheel lands on 4. Students will receive extra credit points equal to the amount the wheel lands on.
Game 2: A different wheel is spun for this game. It also has values 0, 2 and 4. When it is spun there is a 5% chance that the wheel lands on 0, an 80% chance the wheel lands on 2, and a 15% chance the wheel lands on 4. Students will receive extra credit points equal to the amount the wheel lands on.
1. What is the expected number of points earned by playing each game? Fill in the probability tables below:
Game 1:
Points earned= X / 0 / 2 / 4p(X)
Xp(X)
Expected value of points earned for Game 1 ______
Game 2:
Points earned= X / 0 / 2 / 4P(X)
Xp(X)
Expected value of points earned for Game 2 ______
2. If students played these games every day for the rest of the school year, which statement is most likely to be true:
a) They will earn more points playing Game 1
b) They will earn more points playing Game 2
c) They will earn the same amount of points playing either game.
3. By looking at the two probability tables, answer the following qeustions:
a) Which game (1 or 2) is more likely to result in a student receiving 0 points on a single play?
b) Which game (1 or 2) is more likely to result in a student receiving the big 4 point bonus on a single play?
c) Which game (1 or 2) is more likely to result in students receiving some bonus points on a single play?
4. Which game (1 or 2) seems to involve more risk for the player playing it on any single day? Explain your answer.