A and B are mutually exclusive events. The probability of occurrence of A is \(\displaystyle\frac{3}{5}\) and the probability of occurrence of B is \(\displaystyle\frac{1}{3}\). What is the probability of both A and B occurring at the same time?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
Mutually exclusive events cannot happen together: if one occurs, the other cannot. So the event “A and B both occur” is impossible, and its probability is 0, whatever the separate probabilities of A and B are.
\(P(A\cap B)=0\)
Tip: \(\frac{3}{5}+\frac{1}{3}=\frac{14}{15}\) (Option (1)) is the probability that A or B occurs; for mutually exclusive events, probabilities are added for “or”, never for “and”.