SOLUTION: Suppose a certain game is fair and costs $3 if you lose and has a net payoff of $7 if you win. The only possible outcomes of the game are winning and losing. What is the probabilit

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Question 1127159: Suppose a certain game is fair and costs $3 if you lose and has a net payoff of $7 if you win. The only possible outcomes of the game are winning and losing. What is the probability of winning?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the probability of winning; then 1-x is the probability of losing.

The game is fair if the expected value is 0.

To find the expected value, find the product of each outcome and its probability and add the products.

There are two possible outcomes: win (value +7, probability x) or lose (value -3, probability (1-x))

%28%2B7%29%28x%29%2B%28-3%29%281-x%29+=+0
7x-3%2B3x+=+0
10x+=+3
x+=+.3

The probability of winning is 0.3, or 30%.