ProbabilityHard
Question
Let 0 < P (A) < 1, 0 < P(B) < 1 and P(A ∪ B) = P(A) + P(B) - P(A)P(B), then
Options
A.P(B / A) = P(B) - P(A)
B.P(A′- B′) = P(A′) - P(B′)
C.P(A ∪ B)′ = P(A)′ P(B)′
D.P(A / B) = P(A) - P(B)
Solution
Since, P(A ∩ B) = P(A).P(B)
It means A and are independent events so A′ and B′ are also independent.
∴ P(A ∪ B)′ = P(A ∩ B)′
= P(A′).P(B′)
It means A and are independent events so A′ and B′ are also independent.
∴ P(A ∪ B)′ = P(A ∩ B)′
= P(A′).P(B′)
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