A game consists of rolling a regular die. You pay $5 to play the game, and the $5 is not returned. If you roll a 1 or 2, you win $6. If you roll a 3, 4, 5, or 6, you win nothing. What is the mean value for this game, taking into account the $5 cost of the game?
A) −$5
B) −$3
C) $1
D) $3

Question

Quizplus · Accepted Answer

The mean value of a game can be calculated by subtracting the cost of the game from the weighted average of the possible outcomes. 
For this game, there are two winning outcomes with a probability of 1/3 each, and two losing outcomes with a probability of 1/6 each. 
This gives a mean value of: 
(1/3 x $6) + (1/3 x $6) + (1/6 x $0) + (1/6 x $0) - $5 = -$3 
Therefore, the best choice is B.

A Game Consists of Rolling a Regular Die