Question

Mark the correct alternative in each of the following:

A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is

(a) $\frac{2}{3}$ (b) $\frac{1}{6}$ (c) $\frac{1}{3}$ (d) $\frac{11}{30}$ [CBSE 2014]

Answer 1

Total number of outcomes = 30

The prime numbers from 1 to 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

So, the favourable number of outcomes are 10.

∴ P(selected number is a prime number) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{10}{30}=\frac{1}{3}$

Hence, the correct answer is option C.