Q#31: Rolling 9s for $50

Suppose you are playing a game where there are two fair six-sided dice, and every time you roll the dice and they add up to 9, you win $50. However, to roll the dice costs $20 to play. Is this a game you’re willing to play?

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ANSWER

This questions tests your knowledge of statistics particularly probability theory involving expected values/outcomes.

The concept is rather simple, calculate the probability of rolling a 9 with 2-dice and multiply it by +50 (for the $50 won) added to the probability of not rolling a 9 multiplied by -20 (for the $20 paid). The ways to roll a combined 9 are (3,6), (6,3), (4,5), (5,4) out of the total 36 possible outcomes, or 1/9th. Therefore the expected value/outcome is as follows:

E[X] = 1/9*50 + 8/9*-20 = -12.22

Thus, in this game that we should NEVER play we are expected to lose $12.22 on average.