Question

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

Options

• \[\frac{13}{32}\]

   

•  \[\frac{1}{4}\]

   

•  \[\frac{1}{32}\]

   

• \[\frac{3}{16}\]

   

Answer 1

\[ \frac{13}{32}\]
\[\text{ Here, the three boxes contain 3 white and 1 black }\left( 3W, 1B \right), \text{ 2 white and 2 black }\left( 2W, 2B \right) \text{ and 1 white and 3 black balls } \left( 1W, 3B \right), \text{ respectively } . \]
\[P\left( 2W, 1B \right) = \frac{3}{4} \times \frac{2}{4} \times \frac{3}{4} + \frac{3}{4} \times \frac{2}{4} \times \frac{1}{4} + \frac{1}{4} \times \frac{2}{4} \times \frac{1}{4}\]
\[ = \frac{18}{64} + \frac{6}{64} + \frac{2}{64}\]
\[ = \frac{26}{64}\]
\[ = \frac{13}{32}\]