Question

A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen is prime.

• A. $\frac{1}{4}$
• B. $\frac{27}{100}$
• C. $\frac{26}{100}$
• D. $\frac{6}{25}$

Answer 1

The correct option is A

$\frac{1}{4}$

Given, there are $25$ prime numbers in the set of the first $100$ natural numbers.
They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89 and 97.
We know that, probability of an event E, P(E) =$\frac{\text{number of favourable outcomes}}{\text{total number of all possible outcomes}}$

Here, the number of favourable outcomes = $25$ and the number of all possible outcomes = $100$.
Hence, the probability that the number chosen is prime = $\frac{25}{100}$ = $\frac{1}{4}$.