A coin is tossed three times. In a gambling game, a man is paid $10 if he gets all heads or all tails and he pays out $6 if either 1 or 2 heads show in throwing a coin. What is his expected gain?
listing the possible outcomes
hhh ... +10
hht ... -6
hth ... -6
htt ... -6
thh ... -6
tht ... -6
tth ... -6
ttt ... +10
sum the results to find expected gain