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JEE Main · 2008 · 27 Apr 2008 · Offline · Probability

It is given that the events

A

and

B

are such that

P (A) = \frac{1}{4}, P (\frac{A}{B}) = \frac{1}{2}

and

P (\frac{B}{A}) = \frac{2}{3}

. Then

P (B)

is

(A) $\frac{1}{6}$
(B) $\frac{1}{3}$ ✓ Correct
(C) $\frac{2}{3}$
(D) $\frac{1}{2}$

Answer: (B)

Solution

From

P (B ∣ A) = \frac{P ( A \cap B )}{P ( A )} = \frac{2}{3}

with

P (A) = \frac{1}{4}

, the joint probability is

P (A \cap B) = \frac{2}{3} \times \frac{1}{4} = \frac{1}{6}

. Then

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )} = \frac{1}{2}

gives

P (B) = \frac{1/6}{1/2} = \frac{1}{3}

.

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option

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