A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black bal

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Solution

Q.
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is [2024]

1 $\frac{2}{5}$

2 $\frac{1}{7}$

3 $\frac{1}{5}$

4 $\frac{2}{7}$

Ans.
(4)

The balls can be distributed as (2W, 6B), (3W, 5B), (4W, 4B), (5W, 3B), (6W, 2B)

$∴$ $Required probability$ $= \frac{\frac{{}^{4}C_{2} \times {}^{4}{C_{2}}}{\frac{{}^{8}{C_{4}}}{2 ({}^{2}{C_{2} \times {}^{6}{C_{2}}}) + (2) ({}^{3}{C_{2} \times {}^{5}{C_{2}}}) + {}^{4}{C_{2}} \times {}^{4}{C_{2}}}}}{{}^{8}{C_{4}}}$

$= \frac{6 \times 6}{2 (15) + 2 (30) + 36} = \frac{36}{30 + 60 + 36} = \frac{36}{126} = \frac{2}{7}$

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