A biased coin is tossed repeatedly until a tail appears for the first time. Heads is 3 times as likely to appear as tails. Let x be the number of tosses required. Assume that all the trials of tossing a biased coin are independent. Then, the conditional probability that x ≥ 6 , given that x 3 , is equal to

Question

A biased coin is tossed repeatedly until a tail appears for the first time. Heads is 3 times as likely to appear as tails. Let x be the number of tosses required. Assume that all the trials of tossing a biased coin are independent. Then, the conditional probability that x ≥ 6 , given that x > 3 , is equal to, 9 16, 1 16, 1 2, 3 5

MARKS App · Accepted Answer

P H = 3 4 , P T = 1 4 P x ≥ 6 x > 3 = P x ≥ 6 ∩ x > 3 P x > 3 = P x ≥ 6 P x ≥ 4 P x ≥ 6 = 3 4 5 1 4 + 3 4 6 1 4 + 3 4 7 1 4 + . . . . = 3 4 5 1 4 1 - 3 4 = 3 4 5 P x ≥ 4 = 3 4 3 1 4 + 3 4 4 1 4 + 3 4 5 1 4 + . . . . . . = 3 4 3 1 4 1 - 3 4 = 3 4 3 P x ≥ 6 x > 3 = 3 4 2 = 9 16

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