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(D) Let $P(A)$ and $P(B)$ be the probabilities of events $A$ and $B$ respectively.The probability that exactly one of them occurs is given by $P(A) +

Vedclass · Accepted Answer

$0.10$

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(D) Let $P(A)$ and $P(B)$ be the probabilities of events $A$ and $B$ respectively.The probability that exactly one of them occurs is given by $P(A) + P(B) - 2P(A \cap B) = \frac{2}{5}$.The probability that $A$ or $B$ occurs is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{1}{2}$.Subtracting the first equation from the second equation:$(P(A) + P(B) - P(A \cap B)) - (P(A) + P(B) - 2P(A \cap B)) = \frac{1}{2} - \frac{2}{5}$.$P(A \cap B) = \frac{5 - 4}{10} = \frac{1}{10} = 0.10$.

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 that both of them occur together is:

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