A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6, you lose $1. Calculate the expected winnings.
A)$0.00
B)$1.00
C)$0.50
D)$0.25

Question

Quizplus · Accepted Answer

The expected winnings can be calculated by multiplying each outcome by its probability and summing these products. For rolling a 1 or 2, the probability is 2/6 (or 1/3), and the winnings are $2, so the expected winnings for this outcome are (1/3)*$2 = $2/3. For rolling a 3, 4, 5, or 6, the probability is 4/6 (or 2/3), and the loss is $1, so the expected loss for this outcome is (2/3)*(-$1) = -$2/3. Adding these together, $2/3 - $2/3 = $0.00, which means the expected winnings are $0.00.

A Fair Die Is Rolled