It is given the events $A$ and $B$ are such that $P(A) = \frac{1}{4},P\left( A \middle| B \right) = \frac{1}{2}and\ P\left( B \middle| A \right) = \frac{2}{3}$.Then, $P(B)$ is

Question

Dr. Abubacker · Accepted Answer

(c)
We know, $P\left( \frac{A}{B} ight) = \frac{P(A \cap B)}{P(B)}$
and $P\left( \frac{B}{A} ight) = \frac{P(B \cap A)}{P(A)}$
$	herefore P(B) = \frac{P\left( \frac{B}{A} ight).P(A)}{P\left( \frac{A}{B} ight)}$
$= \frac{\left( \frac{2}{3} ight)\left( \frac{1}{4} ight)}{\left( \frac{1}{2} ight)} = \frac{1}{3}$

Q. It is given the events $A$ and $B$ are such that $P(A) = \frac{1}{4},P\left( A \middle| B \right) = \frac{1}{2}and\ P\left( B \middle| A \right) = \frac{2}{3}$.Then, $P(B)$ is

Explanation

Reviewed by Dr. Abubacker

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