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Proven Potential TMUA Sample Paper 1 · Q13

Paper 1ProbabilitySequences & seriesNumber & counting

Two players, A and B, play a series of games. Each game is independent, and player A has a probability p=23p=\frac23 of winning any single game. The match ends as soon as player A wins two games in a row. Find the probability that player A wins the match within the first nn games, where nn is a positive integer.

A1−43(23)n+13(−13)n1-\frac43\left(\frac23\right)^n+\frac13\left(-\frac13\right)^n
B1−(1−49)n1-\left(1-\frac49\right)^n
C1−(13)n1-\left(\frac13\right)^n
D49\frac49

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