For two events A and B,if P(A cup B) = frac{3 | vedclass

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(A) Given $P(A') = \frac{2}{3}$,we find $P(A) = 1 - P(A') = 1 - \frac{2}{3} = \frac{1}{3}$.Using the addition theorem for probability,$P(A \cup B) = P

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$5/12$

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(A) Given $P(A') = \frac{2}{3}$,we find $P(A) = 1 - P(A') = 1 - \frac{2}{3} = \frac{1}{3}$.Using the addition theorem for probability,$P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the values: $\frac{3}{4} = \frac{1}{3} + P(B) - \frac{1}{4}$.Solving for $P(B)$: $P(B) = \frac{3}{4} + \frac{1}{4} - \frac{1}{3} = 1 - \frac{1}{3} = \frac{2}{3}$.We know that $P(A' \cap B) = P(B) - P(A \cap B)$.Therefore,$P(A' \cap B) = \frac{2}{3} - \frac{1}{4} = \frac{8 - 3}{12} = \frac{5}{12}$.

For two events $A$ and $B$,if $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(A') = \frac{2}{3}$,then find $P(A' \cap B)$.

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