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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

Options

  1. A9 16
  2. B1 16
  3. C1 2
  4. D3 5

Correct answer

A. 9 16

Step-by-step solution

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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