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A gambler plays a dice game where a pair of fair dice are rolled one time...

A gambler plays a dice game where a pair of fair dice are rolled one time and the sum is recorded. The gambler will continue to place $2 bets that the sum is 6, 7, 8, or 9 until she has won 7 of these bets. That is, each time the dice are rolled, she wins $2 if the sum is 6, 7, 8, or 9 and she loses $2 each time the sum is not 6, 7, 8, or 9 and she keeps playing like this until she's won 7 times.

a. What's the probability she places a total of 12 bets?

b. What's her expected winnings when she stops?

Math   Statistics-And-Probability   
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Answer #1

Outcomes when two dice are rolled :

Sum when two dice are rolled :

(a)

(b)

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