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Let A , B and C be three events, which are pair-wise independent and E ¯ denotes the complement of an event E . If P A ∩ B ∩ C = 0 and P C > 0 , then P A ¯ ∩ B ¯ | C is equal to

Options

  1. AP A ¯ - P B
  2. BP A ¯ - P B ¯
  3. CP A ¯ + P B ¯
  4. DP A + P B ¯

Correct answer

A. P A ¯ - P B

Step-by-step solution

P A ¯ ∩ B ¯ | C = P A ¯ ∩ B ¯ ∩ C P C = P C - P A ∩ C - P B ∩ C + P A ∩ B ∩ C P C = P C - P A P C - P B P C P C = 1 - P A - P B = P A ¯ - P B or P B ¯ - P A

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