A bag contains 13 white and 7 black balls. Two balls are drawn at random. What is the probability that they are of the same colour?

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$\frac{41}{190}$

$\frac{21}{190}$

$\frac{59}{190}$

$\frac{99}{190}$

answer is D.

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Detailed Solution

Total possible outcomes

$=^{20} C_{2} = \frac{20 \times 19}{1 \times 2} = 190$

Total favorable outcomes

$\begin{array}{l} =^{13} C_{2} +^{7} C_{2} = \frac{13 \times 12}{1 \times 2} + \frac{7 \times 6}{1 \times 2} \\ = 78 + 21 = 99 \end{array}$

$∴$ Required probability $= \frac{99}{190}$

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