If two events E1 and E2 are mutually exclusive, which expression gives P(E1 ∪ E2)?

If two events E1 and E2 are mutually exclusive, which expression gives P(E1 ∪ E2)?

• A. P(E1) × P(E2)
• B. P(E1) + P(E2)
• C. P(E1) − P(E2)
• D. max(P(E1), P(E2))

Answer: (B)

When two events cannot happen at the same time, their intersection has probability zero: P(E1 ∩ E2) = 0. The probability that at least one of them happens is given by the inclusion-exclusion principle: P(E1 ∪ E2) = P(E1) + P(E2) − P(E1 ∩ E2). Since the intersection is zero, this reduces to P(E1) + P(E2). That’s why the sum is the correct expression. For contrast, multiplying would correspond to a scenario where you’re looking at both events happening together (which isn’t possible here), and subtracting or taking a maximum don’t reflect the probability of "either" happening. For a quick check, if P(E1) = 0.4 and P(E2) = 0.2, then P(E1 ∪ E2) = 0.6.

When two events cannot happen at the same time, their intersection has probability zero: P(E1 ∩ E2) = 0. The probability that at least one of them happens is given by the inclusion-exclusion principle: P(E1 ∪ E2) = P(E1) + P(E2) − P(E1 ∩ E2). Since the intersection is zero, this reduces to P(E1) + P(E2). That’s why the sum is the correct expression.

For contrast, multiplying would correspond to a scenario where you’re looking at both events happening together (which isn’t possible here), and subtracting or taking a maximum don’t reflect the probability of "either" happening. For a quick check, if P(E1) = 0.4 and P(E2) = 0.2, then P(E1 ∪ E2) = 0.6.