Q. A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour, is
A) $\frac{14}{15}$
B) $\frac{11}{15}$
C) $\frac{7}{15}$
D) $\frac{4}{15}$
Explanation
(c)
Probability that both are of red colours$= \frac{\ ^{8}C_{2}}{\ ^{15}C_{2}} = \frac{4}{15}$
And probability that both are of black colours
$= \frac{\ ^{7}C_{2}}{\ ^{13}C_{2}} = \frac{3}{15}$
$\therefore$Probability that they are of same colour
$= \frac{4}{15} + \frac{3}{15} = \frac{7}{15}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.