If A and B are any two events,then the probab | vedclass

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(B) The probability that exactly one of the events $A$ or $B$ occurs is given by the probability of the symmetric difference of $A$ and $B$,denoted as

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$P(A) + P(B) - 2P(A \cap B)$

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(B) The probability that exactly one of the events $A$ or $B$ occurs is given by the probability of the symmetric difference of $A$ and $B$,denoted as $P(A \Delta B)$.This is equivalent to the probability that $A$ occurs and $B$ does not,or $B$ occurs and $A$ does not:$P(A \cap \bar{B}) + P(\bar{A} \cap B)$Using the property $P(A \cap \bar{B}) = P(A) - P(A \cap B)$ and $P(\bar{A} \cap B) = P(B) - P(A \cap B)$:$= (P(A) - P(A \cap B)) + (P(B) - P(A \cap B))$$= P(A) + P(B) - 2P(A \cap B)$.

If $A$ and $B$ are any two events,then the probability that exactly one of them occurs is

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