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Q.

Three boxes numbered $I, I I, I I I$ contain balls as follows
WHITE BLACK RED
I 1 2 3
II 2 1 1
III 4 5 3
One box is selected and a ball is drawn from it if the ball is red then probability that it is from box II.

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a

$\frac{1}{9}$

b

$\frac{1}{2}$

c

$\frac{1}{3}$

d

$\frac{1}{4}$

answer is C.

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Detailed Solution

$\begin{array}{l} P (A_{1}) = P (A_{2}) = P (A_{3}) = \frac{1}{3} \\ P (E / A_{1}) = \frac{3}{6} = \frac{1}{2} P (\frac{E}{A_{2}}) = \frac{1}{4}, P (\frac{E}{A_{3}}) = \frac{3}{12} = \frac{1}{4} \\ P (\frac{A_{2}}{E}) = \frac{P (A_{2}) . P (E / A_{2})}{\sum_{I = 1}^{3} P (A_{i}) P (\frac{E}{A_{I}})} = \frac{1}{4} \end{array}$

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