Question

A box contains 5 red balls, 6 white balls and 9 black balls. Two balls are drawn at random. (The first ball is not replaced). Find the probability that both balls are of the same colour.

Answer 1

Number of red balls =5

Number of White balls =6

Number of Black balls =9

Total Number of balls =20

Probability that both balls are of the same color-

$P=\dfrac{^5C_2}{^{20}C_2}+\dfrac{^6C_2}{^{20}C_2}+\dfrac{^9C_2}{^{20}C_2}$

$=\dfrac{20}{380}+\dfrac{30}{380}+\dfrac{72}{380}\\[9pt]=\dfrac{122}{380}=0.3210$