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(A) Let $W$ denote a white ball and $B$ denote a black ball. The contents of the boxes are: Box $I$: $3W, 1B$ (Total $4$ balls) Box $II$: $2W, 2B$ (To

Vedclass · Accepted Answer

$13/32$

Vedclass · Answer

(A) Let $W$ denote a white ball and $B$ denote a black ball. The contents of the boxes are: Box $I$: $3W, 1B$ (Total $4$ balls) Box $II$: $2W, 2B$ (Total $4$ balls) Box $III$: $1W, 3B$ (Total $4$ balls) We need to draw $2$ white and $1$ black ball. This can happen in three mutually exclusive ways: $1$. Box $I$ gives $B$,Box $II$ gives $W$,Box $III$ gives $W$ $2$. Box $I$ gives $W$,Box $II$ gives $B$,Box $III$ gives $W$ $3$. Box $I$ gives $W$,Box $II$ gives $W$,Box $III$ gives $B$ The required probability is: $P = P(B_I)P(W_{II})P(W_{III}) + P(W_I)P(B_{II})P(W_{III}) + P(W_I)P(W_{II})P(B_{III})$ $P = (\frac{1}{4} 	imes \frac{2}{4} 	imes \frac{1}{4}) + (\frac{3}{4} 	imes \frac{2}{4} 	imes \frac{1}{4}) + (\frac{3}{4} 	imes \frac{2}{4} 	imes \frac{3}{4})$ $P = \frac{2}{64} + \frac{6}{64} + \frac{18}{64} = \frac{26}{64} = \frac{13}{32}$

Three boxes contain respectively $3$ white and $1$ black,$2$ white and $2$ black,$1$ white and $3$ black balls. From each of the boxes,one ball is drawn at random. The probability that $2$ white and $1$ black balls will be drawn is:

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