A bag contains 18

(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.