A bag contains some balls of which x are white, 2x are black are 3x are red. A ball is selected at random.
A bag contains some balls of which x are white, 2x are black are 3x are red. A ball is selected at random. What is the probability that it is
(i) not red?
(ii) white?
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 $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{x}{6 x}=\frac{1}{6}$