If A and B are arbitrary events, then

Engineering

Mathematics

Conditional Probability

Question

P(A∩B) ≥ P(A) + P(B)

P(A∩B) ≤ P(A) + P(B)

P(A∩B) = P(A) + P(B)

none of these

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For arbitrary events A, B, we have
P(A∪B) = P(A) + P(B) − P(A∩B). ...(1)
Since probability of an event is a non-negative quantity, equation (1) gives

P(A) + P(B) − P(A∩B) ≥ 0
or P(A) + P(B) ≥ P(A∩B)
or P(A∩B) ≤ P(A) + P(B).

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