2 players A , B tosses a fair coin in cyclic order A , A , B , A , A , B … till a head appears. If the probability that A gets head first is p , then 24 p is equal to

Question

2 players A , B tosses a fair coin in cyclic order A , A , B , A , A , B … till a head appears. If the probability that A gets head first is p , then 24 p is equal to,

MARKS App · Accepted Answer

Required probability = A + A - A + A - A - B - A + A - A - B - A - A + A - A - B - A - A - B - A = 1 2 + 1 2 2 + 1 2 4 + 1 2 5 + 1 2 7 + 1 2 8 + 1 2 10 + … = 1 2 + 1 2 4 + 1 2 7 + 1 2 10 + … + 1 2 2 + 1 2 5 + 1 2 8 + … = 1 2 1 - 1 8 + 1 4 1 - 1 8 = 4 7 + 2 7 = 6 7 = p Hence, 24 p = 24 × 7 6 = 28

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