A box contains 4 balls, 2 balls are drawn from it and are found to be white, the probability that all the balls in the box are white is

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$\frac{3}{5}$

$\frac{1}{5}$

$\frac{4}{5}$

$\frac{2}{5}$

answer is B.

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Detailed Solution

Required probability $= \frac{P (all white)}{P (2 w) + P (3 w) + P (4 w)}$

$= \frac{\frac{{}^{4}C_{2}}{{}^{4}C_{2}}}{\frac{{}^{2}C_{2}}{{}^{4}C_{2}} + \frac{{}^{3}C_{2}}{{}^{4}C_{2}} + \frac{{}^{4}C_{2}}{{}^{4}C_{2}}} = \frac{1}{\frac{1}{6} + \frac{1}{2} + 1} = \frac{3}{5}$

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