A game involving a pair of dice pays you $4 with probability 16/36, costs you $2 with probability 14/36, and costs you $6 with probability 6/36.
If you play this game many times, in the long run how will your actual average gain per play compare with your answer to the previous question?
A) smaller
B) bigger
C) about the same
D) The question can't be answered.

Question

Quizplus · Accepted Answer

By calculating the expected value of this game, we get:

E(X) = (16/36)($4) + (14/36)($-2) + (6/36)($-6) = $0.44

This means that on average, you can expect to gain $0.44 per play in the long run. Since this value is higher than $0 (meaning that on average, you'll make some money per play), your actual average gain per play will likely be lower due to fluctuations in individual outcomes. However, the overall average should still be close to $0.44, so the answer is about the same.

A Game Involving a Pair of Dice Pays You $4