If A and B are two events such that P(A)=frac | vedclass

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(A) Given $P(A)=\frac{1}{3}$,$P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$.We need to find $P(A^{\prime} | B)$.Using the formula for conditional pr

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$\frac{2}{3}$

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(A) Given $P(A)=\frac{1}{3}$,$P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$.We need to find $P(A^{\prime} | B)$.Using the formula for conditional probability,$P(A^{\prime} | B) = \frac{P(A^{\prime} \cap B)}{P(B)}$.Since $P(A^{\prime} \cap B) = P(B) - P(A \cap B)$,$P(A^{\prime} | B) = \frac{P(B) - P(A \cap B)}{P(B)}$.Substituting the values:$P(A^{\prime} | B) = \frac{\frac{1}{2} - \frac{1}{6}}{\frac{1}{2}} = \frac{\frac{3-1}{6}}{\frac{1}{2}} = \frac{\frac{2}{6}}{\frac{1}{2}} = \frac{1}{3} 	imes 2 = \frac{2}{3}$.

If $A$ and $B$ are two events such that $P(A)=\frac{1}{3}$,$P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$,then $P(A^{\prime} | B)$ is

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