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.
Answers
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