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tmua.me Medium Set E Paper 1 · Q8

Paper 1Probability

Players AA and BB play games until one of them has won two games. There are no draws. In each game, AA has probability 2/32/3 of winning, independently of the results of the other games.

Given that AA wins the contest, what is the probability that three games were played?

A14\dfrac14
B827\dfrac8{27}
C25\dfrac25
D49\dfrac49
E23\dfrac23

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