If P(AB) = P(A)P(B),P(A/B) = 1/4,and P(B/A) = | vedclass

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(C) Given that $P(AB) = P(A)P(B)$,it implies that events $A$ and $B$ are independent.For independent events,$P(A/B) = P(A)$.Given $P(A/B) = 1/4$,there

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$P(AB) = 1/12$

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(C) Given that $P(AB) = P(A)P(B)$,it implies that events $A$ and $B$ are independent.For independent events,$P(A/B) = P(A)$.Given $P(A/B) = 1/4$,therefore $P(A) = 1/4$.Similarly,$P(B/A) = P(B)$.Given $P(B/A) = 1/3$,therefore $P(B) = 1/3$.Now,calculate $P(AB)$:$P(AB) = P(A) 	imes P(B) = (1/4) 	imes (1/3) = 1/12$.Also,calculate $P(A'B')$:Since $A$ and $B$ are independent,$A'$ and $B'$ are also independent.$P(A'B') = P(A')P(B') = (1 - P(A))(1 - P(B)) = (1 - 1/4)(1 - 1/3) = (3/4)(2/3) = 6/12 = 1/2$.Comparing with the options,$P(AB) = 1/12$ is correct.

If $P(AB) = P(A)P(B)$,$P(A/B) = 1/4$,and $P(B/A) = 1/3$,then which of the following is true?

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