Question

A bag contains $8$ red and $7$ black balls. Two baIls are drawn at random. The probability that both the baIls are ofthe same colour is

• A. $\frac{14}{15}$
• B. $\frac{11}{15}$
• C. $\frac{7}{15}$
• D. $\frac{4}{15}$

Answer 1

Answer: (C)

$\frac{7}{15}$

Here total number of balls in bag = 15
Probability that both the balls are of same colour
= P(both red) + (both black)
$\therefore \frac{{}^8{C}_2}{{}^{15}{C}_2}+\frac{{}^7{C}_2}{{}^{15}{C}_2}$
or $P=\frac{4}{15}+\frac{3}{15}=\frac{7}{15}$