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Question
If A and B′ are independent events, then P(A' ∪ B) = 1 – P (A) P(B')
Options
True
False
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Solution
This statement is True.
Explanation:
P(A' ∪ B') = P(A') + P(B) – P(A' ∩ B)
= P(A') + P(B) – [P(B) – P(A ∩ B)]
= 1 – P(A) + P(B) – P(B) – P(A)P(B)
= 1 – P(A) – P(A)P(B)
= 1 – P(A)(1 – P(B))
= 1 – P(A)P(B')
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