SOLUTION: A certain game involves tossing 3 fair coins. It pays 25 cents for 3 heads, 15 cents for 2 heads, and 6 cents for 1 head. What is a fair price to pay to play this game?

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Question 1138271: A certain game involves tossing 3 fair coins. It pays 25 cents for 3 heads, 15 cents for 2 heads, and 6 cents for 1 head. What is a fair price to pay to play this game?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The probability to have 3 heads is %281%2F2%29%5E3 = 1%2F8.


The probability to have 2 heads is C%5B3%5D%5E2%2A%281%2F2%29%5E3 = 3%2F8.


The probability to have 1 heads is C%5B3%5D%5E1%2A%281%2F2%29%5E3 = 3%2F8.


The mathematical expectation of the winning amount of this game is



    25%2A%281%2F8%29 + 15%2A%283%2F8%29 + 6%2A%283%2F8%29 = %2825%2B3%2A15%2B6%2A3%29%2F8 = %2888%2F8%29 = 11 cents.