Question

A bag contains $18$ balls out of which $x$ balls are red.
If $2$ more red balls are put in the bag, the probability of drawing a red will be $\frac{9}{8}$ times the probability of drawing in the first case. Find the value of $x$.

Answer 1

Total No . of Observations = 18
No . of Red Balls = x
Probability of Red Ball = Favourable Observations / Total No. of Observations
P(of Red Ball) = x/18
Two Red Balls Are Added
Updated No . of Red Balls = x + 2
Total no of Balls = 18 + 2 = 20
P(of red Ball) = x + 2 / 20
P(updated red balls) is 9/8 times of P(initial red balls)
9/8 * x/18 = (x + 2)/20
x / 16 = (x + 2)/20
(x / 16) * 20 = x + 2
5x / 4 = x + 2
5x = 4x + 8
5x - 4x = 8
x = 8
Therefore,
Initial No.Of Red Balls = 8