# A number is chosen from 1 to 20. Find the probability that the number chosen is a prime number.

Last updated date: 19th Mar 2023

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Answer

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Hint: First of all list down all the prime numbers from 1 to 20 that are 2, 3, 5, 7, 11, 13, 17, 19 and use probability of an event $=\dfrac{\text{Number of favourable cases}}{\text{Number of total cases}}$

Complete step-by-step answer:

Here favourable cases are total prime numbers from 1 to 20 and total cases are total numbers from 1 to 20.

Here we are given that a number is chosen from 1 to 20. We have to find the probability that the number chosen is the prime number.

Before proceeding with the question, we must know some basic terms like prime number, probability etc.

Prime numbers are the numbers that are divisible only by itself and 1. In other words we can say that prime numbers are numbers that have just two factors, 1 and itself.

Examples of prime numbers are 2, 3, 11, 5, 7, 17 etc. We must note that 2 is the only prime number as well even that is 2 is the only even prime number. All other prime numbers are odd.

Also the term ‘probability’ means the extent to which an event is likely to occur measured by ratio of favourable cases to the whole number of cases possible. In short we can say that ‘probability’ means possibility.

Probability of an event $=\dfrac{\text{Number of favourable outcomes/cases}}{\text{Number of total outcomes/cases}}$

Now, to select the prime number from 1 to 20. We must first note down all the prime numbers from 1 to 20.

The numbers that have 2 factors 1 and itself that is prime numbers from 1 to 20 are,

2, 3, 5, 7, 11, 13, 17, 19

Therefore, we have a total 8 prime numbers from 1 to 20.

Now the total numbers from 1 to 20 = 20

Here our favourable case is choosing the prime number from 1 to 20. Therefore, we get the number of favourable cases = 8.

Also here our total cases are all the numbers from 1 to 20. Therefore, the number of total cases = 20.

As we know that,

Probability of an event $=\dfrac{\text{Number of favourable cases}}{\text{Number of total cases}}$,

We get, probability of choosing a prime number from 1 to 20 $=\dfrac{8}{20}=\dfrac{2}{5}$.

Therefore, we get the probability of choosing a prime number from 1 to 20 as $\dfrac{2}{5}or\ 0.4$.

Note: Some students make this mistake of considering all the odd numbers as prime numbers but this is wrong. For example numbers like 9, 15, 21, 25 etc are odd but not prime. So this mistake must be avoided. Also apart from noting each prime number, students can remember that there are a total 25 prime numbers from 1 to 100 and 15 prime numbers from 1 to 50.

Complete step-by-step answer:

Here favourable cases are total prime numbers from 1 to 20 and total cases are total numbers from 1 to 20.

Here we are given that a number is chosen from 1 to 20. We have to find the probability that the number chosen is the prime number.

Before proceeding with the question, we must know some basic terms like prime number, probability etc.

Prime numbers are the numbers that are divisible only by itself and 1. In other words we can say that prime numbers are numbers that have just two factors, 1 and itself.

Examples of prime numbers are 2, 3, 11, 5, 7, 17 etc. We must note that 2 is the only prime number as well even that is 2 is the only even prime number. All other prime numbers are odd.

Also the term ‘probability’ means the extent to which an event is likely to occur measured by ratio of favourable cases to the whole number of cases possible. In short we can say that ‘probability’ means possibility.

Probability of an event $=\dfrac{\text{Number of favourable outcomes/cases}}{\text{Number of total outcomes/cases}}$

Now, to select the prime number from 1 to 20. We must first note down all the prime numbers from 1 to 20.

The numbers that have 2 factors 1 and itself that is prime numbers from 1 to 20 are,

2, 3, 5, 7, 11, 13, 17, 19

Therefore, we have a total 8 prime numbers from 1 to 20.

Now the total numbers from 1 to 20 = 20

Here our favourable case is choosing the prime number from 1 to 20. Therefore, we get the number of favourable cases = 8.

Also here our total cases are all the numbers from 1 to 20. Therefore, the number of total cases = 20.

As we know that,

Probability of an event $=\dfrac{\text{Number of favourable cases}}{\text{Number of total cases}}$,

We get, probability of choosing a prime number from 1 to 20 $=\dfrac{8}{20}=\dfrac{2}{5}$.

Therefore, we get the probability of choosing a prime number from 1 to 20 as $\dfrac{2}{5}or\ 0.4$.

Note: Some students make this mistake of considering all the odd numbers as prime numbers but this is wrong. For example numbers like 9, 15, 21, 25 etc are odd but not prime. So this mistake must be avoided. Also apart from noting each prime number, students can remember that there are a total 25 prime numbers from 1 to 100 and 15 prime numbers from 1 to 50.

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