A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that:
(i) both the balls are white
(ii) one ball is black and the other red

Given is a bag containing 7 white, 5 black and 4 red balls.

By using the formula of probability, we get,

P (E) = favourable outcomes / total possible outcomes

Two balls are drawn at random, so total possible outcomes will be ${}^{16}C_2$

n (S) = 120

(i) Let E be the event of getting both white balls

E = {(W) (W)}

n (E) = 7C2 = 21

P (E) = n (E) / n (S)

= 21 / 120

= 7/40

(ii) Let E be the event of getting one black and one red ball

E = {(B) (R)}

n (E) = 5C14C1 = 20

P (E) = n (E) / n (S)

= 20 / 120

= 1/6