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