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

Solution(By Examveda Team)

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) =   $$\left( {{}^{10}\mathop C\nolimits_2 \times {}^{10}\mathop C\nolimits_2 } \right)$$   $$ = 2 \times {}^{10}\mathop C\nolimits_2 $$   $$ = 2 \times \frac{{10 \times 9}}{{2 \times 1}}$$   = 90
n (S) = number of ways of drawing 2 balls out of 20 balls
$$ = {}^{20}\mathop C\nolimits_2 = \frac{{20 \times 19}}{{2 \times 1}}$$   = 190
$$\therefore P(E) = \frac{{n(E)}}{{n(S)}} = \frac{{90}}{{190}} = \frac{9}{{19}}$$