A game of chance at the carnival costs $4 to play. The player picks a number between 1 and 6 and then three dice are rolled. If the number picked shows on all three dice the player wins $19. If the number picked shows on two of the dice then the player wins $13. If the number shows up once, $9 is won, and if it doesn't show up at all the player owes another $4. What is the player's expected value for this game?
A) -$2.20
B) -$0.51
C) -$3.77
D) $4.67
E) $8.67

Question

Quizplus · Accepted Answer

The expected value is the sum of the probabilities of each outcome multiplied by the value of that outcome. The probability of winning $19 is 1/216, the probability of winning $13 is 3/216, the probability of winning $9 is 6/216, and the probability of losing $4 is 206/216. So the expected value is (1/216) * $19 + (3/216) * $13 + (6/216) * $9 + (206/216) * -$4 = -$2.20.

A Game of Chance at the Carnival Costs $4 to Play