Question

A bag contains 18 balls out of which x are
white.
(i) If one ball is drawn without looking, 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 is
thrice that in (i), find x.
​

Answer 1

GIVEN

A bag contain 18 balls.

The number of white balls is x

TO FIND

1. Probability of getting white ball.

2. If more 6 white balls are added then the probability will thrice of that case 1. Find x

SOLUTION :-

P = Chances/Total Probability

1. Chances of white ball = x

P(Getting a white ball) = x/18

2. After adding six balls

Chances of white ball = x + 6

P(Getting a white ball) = ( x + 6 )/24

*Balls increased to 24

Now, According to the Question :-

(x + 6)/24 = 3 ( x/18)

=> ( x + 6)/24 = x/6

=> 6(x + 6) = 24x

=> 6x + 36 = 24x

=>18x = 36

=> x = 2

Hence the number of white balls is 2 while in case two it was 8.

VERIFICATION

Probability of drawing white ball in case 1 is :-

2/18 = 1/9

In case 2 it is,

8/24 = 1/3

Hence in case 2 it is thrice of case 1 because

1/3 ÷ 1/9 = 3