Question

What is the probability of the event that a number chosen from 1 to 100 is a prime number?
1). $$\dfrac{1}{5}$$
2). $$\dfrac{6}{{25}}$$
3). $$\dfrac{1}{4}$$
4). $$\dfrac{{13}}{{50}}$$

Answer 1

Hint: Here the given question is based on the concept of probability. We have to find the probability of the event choosing a prime number from 1 to 100. For this, first list out the set of prime numbers between the numbers 1 to 100, then by using the definition of probability and on further simplification we get the required probability.

Complete step-by-step solution:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it. Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the probability of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to happen $$P\left( E \right) = \dfrac{\text{Number of favourable outcomes}}{\text{Total Number of outcomes}}$$
Consider the given question:
We need to find the probability of even choosing a prime number from 1 to 100.
Let A be the event of the prime numbers from 1 to 100 are:
$$A = \left\{ {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} \right\}$$
Therefore, total prime numbers from 1 to 100 are = 25.
By, the definition of probability
$$ \Rightarrow \,\,P\left( \text{prime numbers} \right) = \dfrac{\text{Number of prime numbers}}{\text{Total Number of numbers}}$$
$$ \Rightarrow \,\,P\left( \text{Prime numbers} \right) = \dfrac{{25}}{{100}}$$
On simplification, we get
$$\therefore \,P\left( \text{Prime numbers} \right) = \dfrac{1}{4}$$
Hence, the probability of the event that a number chosen from 1 to 100 is a prime number is $$\dfrac{1}{4}$$.
Therefore, option (3) is the correct answer.

Note: Remember, a prime number is defined as the number which has two factors, one and the number itself, students must know at least prime numbers between 1 to 100.
The probability is a number of possible values that must know the definition. We can also find possible numbers by using the permutation concept or combination concept to make the problem easier.