For two mutually exclusive events A and B with probabilities P(A) = 0.3 and P(B) = 0.4, what is P(A ∪ B)?

For two mutually exclusive events A and B with probabilities P(A) = 0.3 and P(B) = 0.4, what is P(A ∪ B)?

• A. 0.7
• B. 0.12
• C. 0.3
• D. 0.4

Answer: (A)

When two events are mutually exclusive, they cannot happen at the same time, so the probability that either occurs is the sum of their probabilities. P(A∪B) = P(A) + P(B) = 0.3 + 0.4 = 0.7. Because there’s no overlap, you don’t subtract anything. The other numbers would represent different ideas—0.12 would be the product of the two probabilities (if you were multiplying for a joint occurrence in some other context), while 0.3 or 0.4 reflect only the chance of one event happening without considering the other. The correct combined probability is 0.7.

When two events are mutually exclusive, they cannot happen at the same time, so the probability that either occurs is the sum of their probabilities. P(A∪B) = P(A) + P(B) = 0.3 + 0.4 = 0.7. Because there’s no overlap, you don’t subtract anything. The other numbers would represent different ideas—0.12 would be the product of the two probabilities (if you were multiplying for a joint occurrence in some other context), while 0.3 or 0.4 reflect only the chance of one event happening without considering the other. The correct combined probability is 0.7.