Question

A bag contains $8$ red and $7$ black balls. Two balls are drawn at random. Find the probability that both the balls are of the same colour.

Answer 1

Total balls $=15$

Number of ways of drawing 2 balls from 15 balls

${=}^{15}{C}_{2}ways$

$=105$ ways

Number of ways of drawing $2$ red balls

${=}^8{C}_2$

$=28$ ways

Number of ways of drawing $2$ black balls

${=}^7{C}_2$

$=21$ ways

Probability of drawing balls of same colour

$=\frac{28+21}{105}$

$=\frac{49}{105}$

Hence, this is the answer.