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  4. A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is

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Q. A bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour, is

EAMCETEAMCET 2007

Solution:

The number of ways to select $2$ balls out of
$10={ }^{10} C_{2}$
Number of ways to select $2$ balls both white $={ }^{6} C_{2}$
Number of ways to select $2$ balls both black $={ }^{4} C_{2}$
$\therefore $ The required probability
$=\frac{{ }^{6} C_{2}+{ }^{4} C_{2}}{{ }^{10} C_{2}}=\frac{7}{15}$