A game involves tossing two coins. If the result is two heads, you win 3 points. If the result is one tail and one head, you win 1 point. If the result is two tails, you lose 5 points. Is this a fair game?

Answer 1

Outcomes:
HH
HT
TH
TT

Prob(2 heads in 2 throws) = (1/2)(1/2) = 1/4
prob(1 h, 1t) = 2/4 = 1/2
prob(2 T) = 1/4

expected value = (1/4)(3) + (1/2)(1) - 5(1/4) = 0

yup, fair game, you can play it all night long