# 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, 2*x *are black are 3*x *are 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 = 2*x*

Number of red balls in the bag = 3*x*

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

∴ Total number of outcomes = 6*x*

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

Favourable number of outcomes = 3*x*

$\therefore \mathrm{P}($ 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 $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{x}{6 x}=\frac{1}{6}$