A bag contains 13 white and 7 black balls. 2 | vedclass

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(D) Total number of balls $= 13 + 7 = 20$.The total number of ways to draw $2$ balls from $20$ is given by the sample space $n(S) = {}^{20}C_{2} = \fr

Vedclass · Accepted Answer

$\frac{99}{190}$

Vedclass · Answer

(D) Total number of balls $= 13 + 7 = 20$.The total number of ways to draw $2$ balls from $20$ is given by the sample space $n(S) = {}^{20}C_{2} = \frac{20 	imes 19}{2 	imes 1} = 190$.For the balls to be of the same colour,they must either both be white or both be black.Number of ways to choose $2$ white balls from $13$ is ${}^{13}C_{2} = \frac{13 	imes 12}{2 	imes 1} = 78$.Number of ways to choose $2$ black balls from $7$ is ${}^{7}C_{2} = \frac{7 	imes 6}{2 	imes 1} = 21$.Total number of favorable outcomes $n(E) = 78 + 21 = 99$.Therefore,the probability $P(E) = \frac{n(E)}{n(S)} = \frac{99}{190}$.

$A$ bag contains $13$ white and $7$ black balls. $2$ balls are drawn at random. What is the probability that they are of the same colour?

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