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

Answer: (D)

$\frac{10}{13}$

Answer 2

Total number of selections of three balls in which balls of both colours are drawn
$=2$ red balls and 1 white ball $+1$ 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
$=\frac{220}{13} C_{3}=\frac{220 \times 6}{13 \times 12 \times 11}=\frac{10}{13}$