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(A) We know that the conditional probability formula is given by $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$.Substituting the given values,we get $P(A \c

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$\frac{1}{3}$

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(A) We know that the conditional probability formula is given by $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$.Substituting the given values,we get $P(A \cap B) = P(B \mid A) 	imes P(A) = \frac{2}{3} 	imes \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$.Now,we use the conditional probability formula for $P(A \mid B)$:$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$.Rearranging for $P(B)$,we get $P(B) = \frac{P(A \cap B)}{P(A \mid B)}$.Substituting the values,$P(B) = \frac{1/6}{1/2} = \frac{1}{6} 	imes 2 = \frac{1}{3}$.

In a random experiment,events $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A \mid B) = \frac{1}{2}$,and $P(B \mid A) = \frac{2}{3}$. Find $P(B)$.

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