SOLUTION: A certain game involves tossing 3 fair coins. It pays 25 cents for 3 heads, 14 cents for 2 heads, and 7 cents for 1 head. What is a fair price to pay to play this game

Algebra ->  Probability-and-statistics -> SOLUTION: A certain game involves tossing 3 fair coins. It pays 25 cents for 3 heads, 14 cents for 2 heads, and 7 cents for 1 head. What is a fair price to pay to play this game       Log On


   

Question 1191268: A certain game involves tossing 3 fair coins. It pays 25 cents for 3 heads, 14 cents for 2 heads, and 7 cents for 1 head. What is a fair price to pay to play this game
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

P(3H) = 1%2F8;

P(2H) = 3%2F8;

P(H)  = 3%2F8.


The math expectation of winning is  25%2A%281%2F8%29+%2B+14%2A%283%2F8%29+%2B+7%2A%283%2F8%29 = %2825%2B14%2A3%2B7%2A3%29%2F8 = 88%2F8 = 11 cents.


So, the fair price to pay to play this game is 11 cents per game.    ANSWER

Solved.