A fair die is rolled. If a number 1 or 2 appears, you will receive $5. If any other number appears, you will pay $2. What is the mean value of one trial of this game?
A) $1/3
B) $3
C) $3/2
D) −$3

Question

Quizplus · Accepted Answer

The mean value is 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 gain is $5, resulting in a contribution of (1/3)*$5 = $5/3. For any other number (3, 4, 5, or 6), the probability is 4/6 (or 2/3), and the loss is $2, resulting in a contribution of (2/3)*(-$2) = -$4/3. Adding these contributions gives $5/3 - $4/3 = $1/3.

A Fair Die Is Rolled