Question

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?

Answer 1

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

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

(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

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