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.

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.