If from each of the three boxes containing 3 | vedclass

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Question

(A) Let $P(W_i)$ and $P(B_i)$ be the probabilities of drawing one white and one black ball from the $i$-th box where $i = 1, 2, 3$ respectively.$P(W_1

Vedclass · Accepted Answer

$\frac{13}{32}$

Vedclass · Answer

(A) Let $P(W_i)$ and $P(B_i)$ be the probabilities of drawing one white and one black ball from the $i$-th box where $i = 1, 2, 3$ respectively.$P(W_1) = \frac{3}{4}, P(B_1) = \frac{1}{4}$$P(W_2) = \frac{2}{4} = \frac{1}{2}, P(B_2) = \frac{2}{4} = \frac{1}{2}$$P(W_3) = \frac{1}{4}, P(B_3) = \frac{3}{4}$Two white and one black ball may be drawn from $3$ boxes in the following three ways:$Way 1$$W, W, B$$Way 2$$W, B, W$$Way 3$$B, W, W$Required probability $= P(W_1)P(W_2)P(B_3) + P(W_1)P(B_2)P(W_3) + P(B_1)P(W_2)P(W_3)$$= (\frac{3}{4} 	imes \frac{2}{4} 	imes \frac{3}{4}) + (\frac{3}{4} 	imes \frac{2}{4} 	imes \frac{1}{4}) + (\frac{1}{4} 	imes \frac{2}{4} 	imes \frac{1}{4})$$= \frac{18}{64} + \frac{6}{64} + \frac{2}{64} = \frac{26}{64} = \frac{13}{32}$.

If from each of the three boxes containing $3$ white and $1$ black,$2$ white and $2$ black,and $1$ white and $3$ black balls,one ball is drawn at random,then the probability that $2$ white and $1$ black ball will be drawn is

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