Posted by **Ann** on Monday, August 17, 2009 at 11:08am.

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?

- Math -
**MathMate**, Monday, August 17, 2009 at 11:28am
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

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