Find the probability that a number selected from the number 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.

Given:

Numbers \( 1,2,3, \ldots, 25 \) are given. Each of the given numbers is equally likely to be selected.

To do:

We have to find the probability that a number selected from the number 1 to 25 is not a prime number.

Solution:

Numbers \( 1,2,3, \ldots, 25 \) are given.

This implies,

The total number of possible outcomes $n=25$.

Prime numbers from 1 to 25 are 2, 3, 5, 7, 11, 13, 17, 19 and 23.

Total number of prime numbers from 1 to 25 $=9$

Total number of non-prime numbers from 1 to 25 $=25-9=16$

Total number of favourable outcomes $=16$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that a number selected from the numbers \( 1,2,3, \ldots, 25 \) is not a prime number $=\frac{16}{25}$

The probability that a number selected from the numbers $1, 2, 3, ........, 25$ is not a prime number is $\frac{16}{25}$.  

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Updated on: 10-Oct-2022

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