Question

The probability that a number selected at random from the numbers $1,2,3,....,99,100$ is a prime is

• A. $0.4$
• B. $0.25$
• C. $0.45$
• D. $0.43$

Answer 1

The correct option is B

$0.25$

Find the required probability:

The given set of numbers is $S=\left\{1,2,3,....,99,100\right\}$.

Thus, $n\left(S\right)=100$.

The set of prime numbers in the given set of numbers can be given by, $P=\left\{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97\right\}$

Thus, $n\left(P\right)=25$.

Hence, the probability that the selected number is a prime number is $P\left(P\right)=\frac{n\left(P\right)}{n\left(S\right)}=\frac{25}{100}=0.25$.

Therefore, the probability that a number selected at random from the numbers $1,2,3,....,99,100$ is a prime is $0.25$.

Hence , correct option is (B).