Discussion
Suppose A and B are mutually exclusive events having probabilities P(A) = 0.25, P(B) = 0.35. What is the probability that A occurs but B does not ?
Answer: B
The probability is 0.25.
Mutually exclusive means \(A \cap B = \emptyset\), so whenever A occurs B does not. Hence
\[ P(A \cap B^{c}) = P(A) - P(A \cap B) = 0.25 - 0 = 0.25 \]
0.1 is \(P(B) - P(A)\), 0.6 is \(P(A \cup B)\), and 0.4 is \(1 - P(A \cup B)\), the chance that neither occurs. None of these is the event 'A but not B'.
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