Given: A bag containing 7 white, 5 black and 4 red balls.
By using the formula,
P (E) = favourable outcomes / total possible outcomes
Two balls are drawn at random, therefore
Total possible outcomes are 16C2
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
(iii) Let E be the event of getting both balls of same colour
E = {(B) (B)} or {(W) (W)} or {(R) (R)}
n (E) = 7C2 + 5C2 + 4C2 = 37
P (E) = n (E) / n (S)
= 37/120
