A bag contains 18 balls out of which x balls are red.

(i) If one ball is drawn at random from the bag, what is the probability that it is not red?


(ii) IF two more red balls are put in the bag, the probability of drawing a red ball will be times the probability of drawing a red ball in the first case. Find the value of x.

(i) Total numbers of elementary events are 18


Let E be the event of getting not red ball


Let A be the event of getting a red ball


The number of favourable events are x


P (red ball) =P (A) = x/18


P (not red ball) = P (E) = 1 – x/18


(ii) Two ball are added to the existing 18 balls


Total numbers of elementary events are: 18 + 2 = 20


Let E be the event of getting a red ball


P (red ball) = P (E) = (x + 2) /20


According to the given condition


(X + 2) /20 = 9/8 x (x/18)


(x + 2) /20 = x/16


4x + 8 = 5x


X = 8 being the initial numbers of red ball.


11