For two events A and B,if P(A) = P(A|B) = fra | vedclass

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(D) Given $P(A) = \frac{1}{4}$ and $P(A|B) = \frac{1}{4}$.Since $P(A|B) = P(A)$,the events $A$ and $B$ are independent.For independent events,$P(B|A)

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(D) Given $P(A) = \frac{1}{4}$ and $P(A|B) = \frac{1}{4}$.Since $P(A|B) = P(A)$,the events $A$ and $B$ are independent.For independent events,$P(B|A) = P(B) = \frac{1}{2}$.Now,check each option:$(a)$ Since $P(A|B) = P(A)$,$A$ and $B$ are independent. This is correct.$(b)$ For independent events,$P(A'|B) = P(A') = 1 - P(A) = 1 - \frac{1}{4} = \frac{3}{4}$. This is correct.$(c)$ For independent events,$P(B'|A') = P(B') = 1 - P(B) = 1 - \frac{1}{2} = \frac{1}{2}$. This is correct.Since all statements are correct,the answer is $(d)$.

For two events $A$ and $B$,if $P(A) = P(A|B) = \frac{1}{4}$ and $P(B|A) = \frac{1}{2}$,then

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