What is the Addition Rule for probabilities when events A and B are mutually exclusive?

What is the Addition Rule for probabilities when events A and B are mutually exclusive?

• A. P(A) + P(B)
• B. P(A) + P(B) − P(A ∩ B)
• C. P(A) × P(B)
• D. 0

Answer: (A)

When two events cannot happen at the same time, the probability that either one occurs is just the sum of their individual probabilities. This follows the Addition Rule in its general form: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). If A and B are mutually exclusive, their intersection is impossible, so P(A ∩ B) = 0. That makes P(A ∪ B) simplify to P(A) + P(B). So the probability of A or B happening is the sum of their probabilities. For example, if A has probability 0.4 and B has probability 0.3, and they cannot happen together, then P(A or B) = 0.4 + 0.3 = 0.7. The other options don’t fit: multiplying probabilities is used for independent events, not for mutually exclusive ones; 0 is not generally the probability of either event; and the expression that subtracts the intersection is the general rule, which becomes P(A) + P(B) in this special case.

When two events cannot happen at the same time, the probability that either one occurs is just the sum of their individual probabilities. This follows the Addition Rule in its general form: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). If A and B are mutually exclusive, their intersection is impossible, so P(A ∩ B) = 0. That makes P(A ∪ B) simplify to P(A) + P(B). So the probability of A or B happening is the sum of their probabilities.

For example, if A has probability 0.4 and B has probability 0.3, and they cannot happen together, then P(A or B) = 0.4 + 0.3 = 0.7.

The other options don’t fit: multiplying probabilities is used for independent events, not for mutually exclusive ones; 0 is not generally the probability of either event; and the expression that subtracts the intersection is the general rule, which becomes P(A) + P(B) in this special case.