ProbabilityHard
Question
Let 0 < P(A) < 1, 0 < P(B) < 1 & P(A ∪ B) = P(A) + P(B) - P(A). P(B), then:
Options
A.P(B/A) = P(B) - P(A)
B.P(AC ∪ BC) = P(AC) + P(BC)
C.P((A ∪ B)C) = P(AC). P(BC)
D.P(A/B) = P(A)
Solution
A & B are independent
P(A ∪ B)c = 1 - P(A ∪ B) = 1 - P(A) - P(B) + P(A ∩ B)
= P
- P(B) + P(A) P(B) = P
- P
P(B)
= P
P
P(A ∪ B)c = 1 - P(A ∪ B) = 1 - P(A) - P(B) + P(A ∩ B)
= P
- P(B) + P(A) P(B) = P - PP(B)= P
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