If A and B be two arbitrary events, then
2017
If A and B be two arbitrary events, then
- A.
P(A ∩ B) = P(A)P(B)
- B.
P(A ∪ B) = P(A) + P(B)
- C.
P(A / B) = P(A ∩ B) + P(B)
- D.
P(A ∪ B) <= P(A) + P(B)
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Correct answer: D
For any two events A and B, the general addition rule states: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Since probabilities are non-negative, P(A ∩ B) ≥ 0. Therefore, subtracting a non-negative value implies: P(A ∪ B) ≤ P(A) + P(B).
This relationship, known as Boole's inequality or the Union Bound, holds true for all arbitrary events.