A box contains 10 black and 10 white balls. What is the probability of drawing 2 balls of the same colour ?

Answer: Option A

Total number of balls = (10 + 10) = 20
Let E be the event of drawing 2 balls of the same colour.
n (E) = number of ways of drawing 2 black balls or 2 white balls.
n (E) =   $$\left({}^{10}{C}_2\times {}^{10}{C}_2\right)$$   $$=2\times {}^{10}{C}_2$$   $$=2\times \frac{10\times 9}{2\times 1}$$   = 90
n (S) = number of ways of drawing 2 balls out of 20 balls
$$={}^{20}{C}_2=\frac{20\times 19}{2\times 1}$$   = 190
$$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{90}{190}=\frac{9}{19}$$