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An observed event B can occur after one of the three events A ₁, ~A ₂, ~A ₃ . If P ( A ₁ )= P ( A ₂ )=0.4, P ( A ₃ )=0.2 and P ( B A ₁ )=0.25, P ( B A ₂ )=0.4 , P ( B A ₃ )=0.125 , what is the probability of A ₁ after observing B?

Options

  1. A1 / 3
  2. B6 / 19
  3. C20 / 57
  4. D2 / 5

Correct answer

C. 20 / 57

Step-by-step solution

aligned & P ( A ₁ ~B )= P ( A ₁ ) P ( B A ₁ ) P ( A ₁ ) P ( B A ₁ )+ P ( A ₂ ) P ( B A ₁ ) & = 0.4 0.25 0.4 0.25+0.4 0.4+0.2 0.125 & = 4 10 25 100 4 10 25 100 + 4 10 4 10 + 2 10 125 1000 = 20 57 aligned

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