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

Question

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

TestHub · Accepted Answer

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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