An urn contains 5 white and 10 red balls 3 balls are drawn a

An urn contains 5 white and 10 red balls. 3 balls are drawn at random one by one without replacement. Find the probability that:

(a) the first ball is white.

(b) the second ball is white given that the first was also white.

(c) the third ball is white given that both the first and second were white.

Solution

There are total 15 balls. There are ¹⁵C₃ ways of selecting 3 balls (of any colours) from 15 balls.

a) p( the first ball is white) = (⁵C₁ * ¹⁰C_² ) / ¹⁵C₂

                                       =( 5 * 45)/105

                                      = 15/7

b) p( the second ball is white/ the first was also white) = 4/14

c) p(the third ball is white / both the first and second were white) = 4/14