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Q.

Boxes B1, B2 and B3, contain balls as given below.
Box White Black
$B_{1}$ 1 2
$B_{2}$ 3 1
$B_{3}$ 2 3
One ball is drawn at random from each box. Then, among the balls drawn, the probability that two are black and one is white, is

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a

$\frac{11}{12}$

b

$\frac{5}{12}$

c

$\frac{7}{12}$

d

$\frac{9}{12}$

answer is A.

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Detailed Solution

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$\begin{matrix} B_{1} & B_{2} & B_{3} & Probability \\ 1 B & 1 B & 1 W & \frac{2}{3} \times \frac{1}{4} \times \frac{2}{5} \\ 1 B & 1 W & 1 B & \frac{2}{3} \times \frac{3}{4} \times \frac{3}{5} \\ 1 W & 1 B & 1 B & \frac{1}{3} \times \frac{1}{4} \times \frac{3}{5} \end{matrix}$

Total Probability $= \frac{4}{60} + \frac{18}{60} + \frac{3}{60} = \frac{25}{60} = \frac{5}{12}$

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