Question

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 is not red? (ii) If 2 more red balls are put in the bag, the probability of drawing a red ball will be 9/8 times the probability of drawing a red ball in the first case. Find the value of x.

Answer 1

Total no . of balls ... 18 ..
Red balls = x
Non red balls = 18-x ....
So answer of (i) is 18-x/18
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Answer 2

Probability of finding a red ball in a draw- x/18.

i) Probability of not finding a red ball in a draw is 1 - x/18 = (18 - x)/18

ii) If two red balls are put in, then there is 20 balls, out of which x + 2 are red.
Probability of drawing a red ball- (x+2)/20.
According to the question,

$\dfrac{x+2}{20} = \dfrac98 \dfrac{x}{18}$
or, $\dfrac{x+2}{5} = \dfrac{x}{4}$
or,$4x + 8 = 5x$
or, $-x = - 8$
or, $x = 8$

So, the answer is x = 8