Question

A bag contains 12 balls of which 'x' are white.
(i) If one ball is drawn at random, what is the probability that it will be a white ball?
(ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in case (i), Find x. [4 MARKS]

Answer 1

Sub-part (i) : 1 Mark
Sub-part (ii) : 3 Marks

A bag contains 12 balls of which 'x' are white.
(i) Probability of drawing a white ball = $\frac{x}{12}$

(ii) 6 more white balls are put in the bag.
New probability of picking a white ball = $\frac{x+6}{18}$

According to question,
Probability of white ball in case (ii) = 2 x probability of white ball in case (i)
Or, $\frac{x+6}{18}$ = $2\times \frac{x}{12}$
Or, $\frac{x+6}{18}=\frac{x}{6}$
Or, $6\times (x+6)=18\times x$
Or, 6x + 36 = 18x
Or, 12x = 36
No. of white balls initially = 3