A game costs 5 to play. A player wins 20 with probability 0.1, wins $8 with probability 0.3, and wins nothing otherwise. What is the…

The expected winnings are the sum of each prize times its probability: $0.1(20) + 0.3(8) + 0.6(0) = 2 + 2.4 + 0 = 4.4$ dollars. The probability of winning nothing is $1 - 0.1 - 0.3 = 0.6$. Subtract the $5 cost to play: $4.4 - 5 = -0.6$. So the player loses an average of $0.60 per game. A common wrong answer is 4.4, which forgets to subtract the cost, so it reports the expected prize rather than the net result. Another is 0.6, which has the correct size but the wrong sign. A third is $-0.5$, from averaging the prizes. Enter a negative number for a loss.