Question

The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is [CBSE 2014]

(a) $\frac{4}{15}$
(b) $\frac{2}{15}$
(c) $\frac{1}{5}$
(d) $\frac{1}{3}$

Answer 1

Total number of outcomes = 15.

Out of the given numbers, multiples of 4 are 4, 8 and 12.

Numbers of favourable outcomes = 3.

∴ P(getting a multiple of 4) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{3}{15}=\frac{1}{5}$

Thus, the probability that a number selected is a multiple of 4 is $\frac{1}{5}$.

Hence, the correct answer is option (c).