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A multiple-choice question has 5 options of which only one is correct. If a student does home work, then he is sure to identify the correct answer, otherwise the answer is chosen at random. Let A be the event that the student does his home work and B be the event that the student answers correctly. If P A = 2 3 , then P A B is equal to

Options

  1. A10 11
  2. B4 5
  3. C3 7
  4. D6 7

Correct answer

A. 10 11

Step-by-step solution

P B A c = 1 5 , P A = 2 3 P A B = P A ∩ B P B = P A ⋅ P B A P A P B A + P A c P B A c = 2 3 × 1 2 3 × 1 + 1 3 × 1 5 = 10 11

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