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Question
If P(A ∪ B) = P(A ∩ B) for any two events A and B, then ______.
Options
P(A) = P(B)
P(A) > P(B)
P(A) < P(B)
None of these
Solution
If P(A ∪ B) = P(A ∩ B) for any two events A and B, then P(A) = P(B).
Explanation:
Given that: P(A ∪ B) = P(A ∩ B)
⇒ P(A) + P(B) – P(A ∩ B) = P(A ∩ B)
⇒ [P(A) – P(A ∩ B)] + [P(B) – P(A ∩ B)] = 0
But P(A) – P(A ∩ B) ≥ 0 ......(i) .......[∵ P(A ∩ B) ≤ P(A) or P(B)]
And P(B) – P(A ∩ B) ≥ 0 ......(ii)
From equation (i) and (ii) we get
P(A) = P(B)
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