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If A and B are two independent events such that P A = 2 3 and P B C = 1 4, then which of the following is false?

Options

  1. AP A A ∪ B = 7 11
  2. BP A ∩ B A c ∩ B c = 0
  3. CP A B = 2 3
  4. DP ( A C ∩ B C ) = 1 12

Correct answer

A. P A A ∪ B = 7 11

Step-by-step solution

P A = 2 3 , P B = 3 4 ∵ A , B are independent events P A ∩ B = P A · P B = 1 2 P A ∪ B = P A + P B - P A ∩ B = 2 3 + 3 4 - 1 2 = 8 + 9 - 6 12 = 11 12 P A A ∪ B = P A ∩ A ∪ B P A ∪ B = P A P A U B = 2 3 11 12 = 8 11 P A ∩ B A ∪ B c = P A ∩ B ∩ A ∪ B C P A ∪ B C = 0 (As A ∩ B   &   A ∪ B C are disjoint) P A B = P A ∩ B P B = 1 2 3 4 = 2 3 P A c ∩ B c = P A ∪ B C = 1 - P A ∪ B = 1

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