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(A) Given that,the probability that exactly one of them occurs is $P(A \cup B) - P(A \cap B) = \frac{2}{5} \dots (i)$ The probability that $A$ or $B$

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$0.1$

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(A) Given that,the probability that exactly one of them occurs is $P(A \cup B) - P(A \cap B) = \frac{2}{5} \dots (i)$ The probability that $A$ or $B$ occurs is $P(A \cup B) = \frac{1}{2} \dots (ii)$ We know that the probability of exactly one event occurring is given by $P(A \cup B) - P(A \cap B)$. Substituting the values from $(i)$ and $(ii)$: $\frac{1}{2} - P(A \cap B) = \frac{2}{5}$ $P(A \cap B) = \frac{1}{2} - \frac{2}{5}$ $P(A \cap B) = \frac{5 - 4}{10} = \frac{1}{10} = 0.1$

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$,then the probability of both of them occurring together is

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