A student plays the following game. He tossed three coins. If he gets exactly two heads he wins $5. If he gets exactly one head he wins $3. Otherwise, he loses $2. On the average, how much should he win or lose per play of the game?
we have that
If he gets exactly two heads he wins $5.
the probability is
P=2/8
If he gets exactly one head he wins $3
the probability is
P=1/8
we have that
2/8+1/8=3/8
that means, that the probaility of any other result is 1-3/8=5/8
therefore
he win or lose per play
(2/8)*$5+(1/8)*$3-(5/8)*$2=(10/8)+(3/8)-(10/8)=3/8=$0.375
the answer is
He win $0.375 per game