Which formula expresses the probability of the union of two events?

• A. P(A ∪ B) = P(A) × P(B)
• B. P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
• C. P(A ∪ B) = P(A ∩ B)
• D. P(A ∪ B) = P(A) + P(B)

Answer: (B)

When you want the probability that at least one of two events occurs, you add the probabilities of each event but must correct for double-counting the part where both happen. That correction is subtracting the probability of both events occurring.

So the formula is: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

If the two events cannot happen together (they are disjoint), the intersection probability is zero and this reduces to P(A) + P(B). The other expressions either ignore the overlap or mix up union with intersection, which isn’t correct in general. For example, the union is not the product of probabilities, and it’s not simply the intersection probability, unless specific conditions apply.