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
(iii) both the balls are of the same colour
given: bag which contains 4 red, 5 black and 7 white balls
formula:
two balls are drawn at random, therefore
total possible outcomes are 16C2
therefore n(S)=120
(i) let E be the event of getting both white balls
E= {(W) (W)}
n(E)= 7C2=21
(ii) let E be the event of getting one black and one red ball
E= {(B) (R)}
n(E)= 5C14C1=20
(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