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A box contains 3 coins B 1 , B 2 , B 3 and the probability of getting heads on the coins are 1 2 , 1 4 , 1 8 respectively. If one of the coins is selected at random and tossed for 3 times and exactly 3 heads appeared, then the probability that it was coin B 1 is

Options

  1. A9 73
  2. B10 73
  3. C36 73
  4. D64 73

Correct answer

D. 64 73

Step-by-step solution

A → selected coin got exactly 3 heads B 1 → coin B 1 is selected B 2 → coin B 2 is selected B 3 → coin B 3 is selected P B 1 = P B 2 = P B 3 = 1 3 Using Bayes Theorem, P B 1 A = P A ∩ B 1 P A = P B 1 ⋅ P A B 1 P B 1 P A B 1 + P B 2 P A B 2 + P B 3 P A B 3 = 1 3 × 1 2 3 1 3 × 1 2 3 + 1 3 × 1 4 3 + 1 3 1 8 3 = 64 64 + 8 + 1 = 64 73

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