A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.

Let S be the sample space

Then n(S) = no of ways of drawing 2 balls out of (6+4) = 10 C 2 10 = 10 * 9 2 * 1 =45

Let E = event of getting both balls of same colour

Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)

                = 6 C 2 + 4 C 2 =  6 * 5 2 * 1 + 4 * 3 2 * 1= 15+6 = 21

Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15