SOLUTION: You play a gambling game with your friend in which you win 60% of the time and lose 40% of the time. When you lose, you lose $1. What profit should you earn when you win in order f

Question 1152680: You play a gambling game with your friend in which you win 60% of the time and lose 40% of the time. When you lose, you lose $1. What profit should you earn when you win in order for the game to be fair? (Round your answer to the nearest cent.)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

m = profit earned after winning
P(winning) = 0.60 is the probability of winning
P(losing) = 0.40
V(winning) = value of winning
V(winning) = m
V(losing) = -1, meaning you lost 1 dollar

E(x) = expected value
E(x) = P(winning)*V(winning) + P(losing)*V(losing)
E(x) = 0.60*m + 0.40*(-1)
E(x) = 0.60*m - 0.40

We want this to be a fair game, so the expected value should be 0
E(x) = 0
0.60*m - 0.40 = 0
0.60*m = 0.40 .......... add 0.40 to both sides
m = 0.40/0.60 .......... divide both sides by 0.60
m = 0.66667 approximately
m = 0.67

When you win the game, the profit should be $0.67 (or 67 cents) to ensure a fair game.

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