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counting and probability intermediate
Problem
Bob and Meena play a two-person game which is won by the first person to accumulate 10 points. At each turn Bob gains a point with probability of . If he doesn't get a point, then Meena gets a point. Meena is now ahead 9 to 8. What is the probability that Meena will win? Express your answer as a common fraction.
Solution
Since Meena has 9 points already, the only way Bob can win is by getting a point on both of the next two turns. The probability that this will happen is . Therefore, the probability that Meena will win is .
Final answer
\frac{8}{9}