# An integer is chosen from the first twenty natural numbers. What is the probability that it is a prime number?

Answer

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Hint: Try to figure out the sample spaces and the number of samples according to the conditions given in the question.

It is given in the question that an integer is chosen from the first twenty natural numbers.

That is,

\[S = \left\{ {1,2,3,4,....20} \right\}\]

Therefore, the total number of samples is $20$

That is,

\[ \Rightarrow n(S) = 20\]

Let us assume $A$ to be an event of getting a prime number.

\[ \Rightarrow A = \left\{ {2,3,5,7,11,13,17,19} \right\}\]

Now, the sample space of prime number contains $8$ samples

That is,

\[ \Rightarrow n(A) = 8\]

Now, let $P(A)$ be the probability of getting a prime number such that

$ \Rightarrow P(A) = \dfrac{{n(A)}}{{n(S)}}$

After substituting the values of \[n(S)\] and \[n(A)\], we get,

$ = \dfrac{8}{{20}} = \dfrac{2}{5}$

Therefore, the probability of a prime number when an integer is chosen from the first twenty natural numbers is $P(A) = \dfrac{2}{5}$.

Note: In these types of questions, find the required sample space and total sample space and put in the probability formula to obtain the answer.

It is given in the question that an integer is chosen from the first twenty natural numbers.

That is,

\[S = \left\{ {1,2,3,4,....20} \right\}\]

Therefore, the total number of samples is $20$

That is,

\[ \Rightarrow n(S) = 20\]

Let us assume $A$ to be an event of getting a prime number.

\[ \Rightarrow A = \left\{ {2,3,5,7,11,13,17,19} \right\}\]

Now, the sample space of prime number contains $8$ samples

That is,

\[ \Rightarrow n(A) = 8\]

Now, let $P(A)$ be the probability of getting a prime number such that

$ \Rightarrow P(A) = \dfrac{{n(A)}}{{n(S)}}$

After substituting the values of \[n(S)\] and \[n(A)\], we get,

$ = \dfrac{8}{{20}} = \dfrac{2}{5}$

Therefore, the probability of a prime number when an integer is chosen from the first twenty natural numbers is $P(A) = \dfrac{2}{5}$.

Note: In these types of questions, find the required sample space and total sample space and put in the probability formula to obtain the answer.

Last updated date: 30th May 2023

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