For two mutually exclusive events A and B, compute $P\(\left\)(A\(\cup\) B\(\right\))$ if $P\(\left\)(A\(\right\))=0.15$ and $P\(\left\)(B\(\right\))=0.32$

• A. 0.048
• B. 0.17
• C. 0.47
• D. 0.53

Answer: (C)

Verified step by step guidance

1. Understand that mutually exclusive events A and B cannot occur at the same time, meaning P(A ∩ B) = 0.
2. Recall the formula for the probability of the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
3. Since A and B are mutually exclusive, substitute P(A ∩ B) = 0 into the formula: P(A ∪ B) = P(A) + P(B).
4. Substitute the given probabilities into the formula: P(A ∪ B) = 0.15 + 0.32.
5. Add the probabilities to find the probability of the union of events A and B.