Solve the problem.
-A certain game involves tossing 3 fair coins. It pays 24 cents for 3 heads, 12 cents for 2 heads, and 4 Cents for 1 head. What is a fair price to pay to play this game?
A) 8 cents
B) 9 cents
C) 13 cents
D) 7 cents

Question

Quizplus · Accepted Answer

The fair price to play the game is the expected value of the payouts. The probability of getting 3 heads (HHH) is (1/2)^3 = 1/8. The probability of getting 2 heads (HHT, HTH, THH) is 3*(1/2)^3 = 3/8. The probability of getting 1 head (HTT, THT, TTH) is also 3*(1/2)^3 = 3/8. The probability of getting no heads (TTT) does not result in a payout and is (1/2)^3 = 1/8, but it's not needed for the calculation of the fair price. The expected payout is thus (1/8)*24 + (3/8)*12 + (3/8)*4 = 3 + 4.5 + 1.5 = 9 cents.

Solve the Problem. -A Certain Game Involves Tossing 3 Fair Coins. It Pays