Question

5. Tanya is considering playing a game at the fair. There are three different ones to choose from, and it costs $2 to play a game. The probabilities associated with the games are given in the table.

Lose $2 Win $1 Win $4
Game 1 0.55 0.20 0.25
Game 2 0.15 0.35 0.50
Game 3 0.20 0.60 0.20

a. What is the expected value for playing each game?





b. If Tanya decides she will play the game, which game should she choose? Explain.

Answer 1

Assuming the cost of playing the game is the same as the two dollars lost (you can't lose more than $2 on a game):

To calculate expected value, multiply each probability by its payout or loss, and add the numbers together:
Game A) 0.10
Game B) 2.05
Game C) 1.00
Since the question is a bit unclear, let's also look at expected value is she has to pay $2 to play, but can also lose an additional $2:
Game A) -1.90
Game B) 0.05
Game C) -1.00
I believe it is the first one, but you may want to clarify with the teacher or a fellow student.

b) If Tanya decides to play a game, she will choose Game B) because this has the highest expected value.