Question

Question 41(i)
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 not red?

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.
$\Rightarrow n\left(S\right)=24$
Let $E_1$= Event of selecting a ball which is not red i.e. can be white or blue.
$\therefore n\left(E_1\right)=\text{Number of white balls+Number~ of blue balls}\Rightarrow n(E_1=8+12=20\therefore \text{Required probability}=\frac{n\left(E_1\right)}{n\left(S\right)}=\frac{20}{24}=\frac{5}{6}$