# A bag contains some balls of which x are white, 2x are black are 3x are red. A ball is selected at random.

Question:

A bag contains some balls of which x are white, 2are black are 3are red. A ball is selected at random. What is the probability that it is

(i) not red?

(ii) white?

Solution:

Number of white balls in the bag = x

Number of black balls in the bag = 2x

Number of red balls in the bag = 3x

Total number of balls in the bag = x + 2x + 3x = 6x

∴ Total number of outcomes = 6x

(i) There are 3x non-red balls (x white balls and 2x black balls) in the bag. So, there are 3x ways to draw a ball from the bag which is not red.

Favourable number of outcomes = 3x

$\therefore \mathrm{P}($ Selected ball is not red $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{3 x}{6 x}=\frac{1}{2}$

(ii) There are x white balls in the bag. So, there are x ways to draw a ball from the bag which is white.

Favourable number of outcomes = x

$\therefore P($ Selected ball is white $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{x}{6 x}=\frac{1}{6}$