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Question
Two events, A and B, will be independent if ______.
Options
A and B are mutually exclusive
P(A′B′) = [1 – P(A)] [1 - P(B)]
P(A) = P(B)
P(A) + P(B) = 1
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Solution
Two events, A and B, will be independent if P(A'B') = [1 − P(A)][1 - P(B)].
Explanation:
A and B are independent
⇒ P (A ∩ B) = P (A) P (B)
and 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))
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