If A and B are two events such that P(A B) = ...

CBSE Class 12 Math 2023 All Sets Solved Paper

Question : 8 of 20

Marks: +1, -0

If A and B are two events such that

P(A\mid B) = 2 \times P(B\mid A)

and

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

then P(B) is equal to:

Solution:

P(A\mid B)=2 \times P(B\mid A)

\Rightarrow \frac{P(A\cap B)}{P(B)} = 2 \times \frac{P(A\cap B)}{P(A)}

\Rightarrow P(A) = 2 \times P(B)

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

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

\Rightarrow P(B) = \frac{2}{9}

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