Question

The probability for a randomly selected number out of 1, 2, 3, 4, …., 25 to be a prime number is:
A. $\dfrac{2}{{25}}$
B. $\dfrac{{23}}{{25}}$
C. $\dfrac{{10}}{{25}}$
D. $\dfrac{9}{{25}}$

Answer 1

Hint:In this question we can easily find the probability of selecting a number to be a prime number. Here we have a total count of numbers of 25. First, we calculate the total number of prime numbers from 1 to 25. Then we will apply the formula of probability to find the required probability.

Complete step-by-step answer:
Probability is defined as the ratio of favorable outcomes to the total number of outcomes in a random experiment.
$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$
First we will count the number of prime numbers between 1 to 25.
Prime numbers between 1 and 25: 2, 3, 5, 7, 11, 13, 17, 19, 23
[Prime numbers are numbers which are divided by 1 and the number itself]
So, Total number of favorable conditions = 9
Total number of outcomes = 25
Probability of selecting a prime number = $\dfrac{9}{{25}}$.

So, the correct answer is “Option D”.

Note:Prime number has only two factors that is 1 and the number itself. For example: 2, 3, 31 etc. Probability involves making predictions about things that may or may not happen. Probability means possibility. There are so many events which cannot be predicted, we can only predict the chance of an event to occur. Probability can be measured within a range of 0 to 1, 0 means that the event is impossible and 1 means event is possible. There are few important terms which are used in probability:
1) Sample Space – it is a set of all the possible outcomes to occur in any trial.
2) Event – It is a set containing the outcome of an experiment.
3) Favorable outcome – Favorable outcome is the outcome of interest.