(C) Total number of balls $= 9 + 7 + 4 = 20$.The number of ways to choose $2$ balls out of $20$ is given by $^{20}C_{2} = \frac{20 \times 19}{2 \times

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(C) Total number of balls $= 9 + 7 + 4 = 20$.The number of ways to choose $2$ balls out of $20$ is given by $^{20}C_{2} = \frac{20 \times 19}{2 \times 1} = 190$.The number of ways to draw one white ball out of $7$ is $^{7}C_{1} = 7$.The number of ways to draw one red ball out of $9$ is $^{9}C_{1} = 9$.The number of favorable outcomes is $^{7}C_{1} \times ^{9}C_{1} = 7 \times 9 = 63$.Therefore,the required probability $= \frac{63}{190}$.

Competitive Quantitative Aptitude Probability Probability

Medium

An urn contains $9$ red,$7$ white and $4$ black balls. If two balls are drawn at random,then the probability that one is white and the other is red is

A
$\frac{18}{95}$
B
$\frac{18}{190}$
C
$\frac{63}{190}$
D
$\frac{91}{190}$

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An urn contains $9$ red,$7$ white and $4$ black balls. If two balls are drawn at random,then the probability that one is white and the other is red is

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