An urn contains five white and ten red balls Three balls are

An urn contains five white and ten red balls. Three 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

(a) the first ball is white.

Number of ways of selecting 4 balls from 5 + 7 + 8 = 20 balls is 20C4 = 4845
Number of ways of selecting four white balls from 5 white balls = 5C4 = 5
Required probability
= Favorable ways / Total ways
= 5C4/20C4
= 5/4845
= 1/969