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

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.

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.