Question

Question 41(ii)
A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is white?

Answer 1

Given that, A bag contains total number of balls=24
A bag contains number of red balls=x
A bag contains number of white balls=2x
and a bag contains number of blue balls=3x
By condition, x+2x+3x=24
$\Rightarrow 6x=24\therefore x=4\therefore \text{Numer of red balls}=x=4\text{Number of white balls}=2x=2\times 4=8\text{and number of blue balls}=3x=3\times 4=12$
So, total number of outcomes for a ball is selected at random in a bag contains 24 balls.
$\Rightarrow n\left(S\right)=24$
Event of selecting a ball which is white
$\therefore n\left(E_2\right)$ =Number of white balls=8
So, required probability=$\frac{n\left(E_2\right)}{n\left(S\right)}=\frac{8}{24}=\frac{1}{3}$