Question

During a game, a balanced die is rolled. A player receives $22 when an even number is rolled, and loses $12 when an odd number is rolled. How much money can he expect on average in the long run?
Is the answer 17?

Answer 1

For a balanced die, the probability of getting an even number is n({2,4,6})/n({1,2,3,4,5,6})=1/2.
Similarly, the probability of getting an odd number is 1/2.
Thus, the expected gain/roll is
expected gain - expected loss
= 0.5*$22 - 0.5*$12
= $11-$6
=$5 per roll on average in the long run