A box contains 6 white balls and 7 black balls. Two balls are drawn at random. What is the probability that both of them are of different colours?

Correct option is D

Given:

White balls = 6, Black balls = 7
Two balls are drawn at random.

Formula Used:

​$$P(\text{Different colours}) = 1 - \left[P(\text{Both white}) + P(\text{Both black})\right]$$​​

Solution:

Total balls = 6 + 7 = 13

​$$P(\text{Both white}) = \frac{{^6C_2}}{{^{13}C_2}},\quad P(\text{Both black}) = \frac{{^7C_2}}{{^{13}C_2}}$$​​

​$$^6C_2 = \frac{6 \times 5}{2} = 15,$$  $$^7C_2 = \frac{7 \times 6}{2} = 21$$​,  $$^{13}C_2 = \frac{13 \times 12}{2} = 78$$​

P(Both same colour ) =$$\frac{15 + 21}{78} = \frac{36}{78} = \frac{6}{13}$$​

P(Different colours) =$$1 - \frac{6}{13} = \frac{7}{13}$$​