Question

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

• A. $\frac{40}{143}$
• B. $\frac{70}{143}$
• C. $\frac{3}{13}$
• D. $\frac{10}{13}$

Answer 1

The correct option is D $\frac{10}{13}$

Total number of selections of three balls in which balls of both colours are drawn.
$=2$ red balls and $1$ white balls $+1$ red ball and $2$ white balls
$={}^8{C}_2\times {}^5{C}_1+{}^8{C}_1\times {}^5{C}_2$
$=140+80=220$
$\therefore$ Required probability
$=\frac{220}{{}^{13}{C}_3}=\frac{220\times 6}{13\times 12\times 11}=\frac{10}{13}$