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प्रश्न
If one ball is drawn at random from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, then the probability that 2 white and 1 black balls will be drawn is
पर्याय
\[\frac{13}{32}\]
\[\frac{1}{4}\]
\[\frac{1}{32}\]
\[\frac{3}{16}\]
उत्तर
\[ \frac{13}{32}\]
\[\text{ Here, the three boxes contain 3 white and 1 black }\left( 3W, 1B \right), \text{ 2 white and 2 black }\left( 2W, 2B \right) \text{ and 1 white and 3 black balls } \left( 1W, 3B \right), \text{ respectively } . \]
\[P\left( 2W, 1B \right) = \frac{3}{4} \times \frac{2}{4} \times \frac{3}{4} + \frac{3}{4} \times \frac{2}{4} \times \frac{1}{4} + \frac{1}{4} \times \frac{2}{4} \times \frac{1}{4}\]
\[ = \frac{18}{64} + \frac{6}{64} + \frac{2}{64}\]
\[ = \frac{26}{64}\]
\[ = \frac{13}{32}\]
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