Which formula expresses P(A ∪ B) in terms of P(A), P(B), and P(A ∩ B)?

• A. P(A) + P(B) - P(A∩B)
• B. P(A) + P(B)
• C. P(A)P(B]
• D. P(A∪B) - P(A∩B)

Answer: (A)

When two events can both happen, you add their probabilities but you must subtract the overlap because that part gets counted twice. This gives P(A ∪ B) = P(A) + P(B) − P(A ∩ B). It accounts for every outcome that lies in A or in B (or both) exactly once.

Adding P(A) and P(B) alone would double-count the overlap. Multiplying probabilities is a rule for independent events, which isn’t specified here. Subtracting P(A ∩ B) from P(A ∪ B) isn’t a correct way to express the union probability.