Question

A game involves tossing two coins. A player wins $1.00 if both tosses result in heads. What should you pay to play this game in order to make it a fair game? Explain your answer.

Answer 1

y = the amount to pay

Coin Winnings Probability Expectation
tosses or losses of this per game
X P(X) X•P(X)
---------------------------------------------
HH $1-y ¼ (1-y)(¼)
HT -y ¼ -y(¼)
TH -y ¼ -y(¼)
TT -y ¼ -y(¼)

Sum of expectations = 0
(1-y)(¼) - y(¼) - y(¼) -y(¼) = 0

Multiply through by 4

(1-y) - y - y - y = 0
1 - y - y - y - y = 0
1 - 4y = 0
-4y = -1
y = ¼ = .25 = 25 cents
This is what I came up with but I don't understand why the sum is 0

Answer 2

there are four different results that can happen. Having both coins tossed as heads is one of the four results that might occur. so there is a one in four chance that you can win $1. Divide $1 by four and you get $0.25, which would make it a fair game.

Answer 3

Cool much more simple then the way I did it - Thanks