Question

what is the probability of the event that a number chosen from 1to 10 is a prime numbers
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Answer 1

I hope it will help you thanks for asking.

Answer 2

To Find : ↴

We have to find the probability of the event that a number chosen from 1 to 10 is a prime numbers.

$\sf \large\orange{So,\: Let's \: Start}$ ↴

$\sf \: Numbers \: from \: 1 \: to \: 10 \: are :$

$\sf \boxed {1, \: 2, \: 3, \: 4, \: 5, \: 6, \: 7, \: 8, \: 9, \: 10}$

$\sf \: What \: are \: Prime \: numbers \: :$ ↴

Before moving to the next step we must know that what are prime numbers. So, Prime numbers are the numbers that is divisible only by itself and 1 only. For Example : 17 , 19, 3, 5, 7, 11 etc.

Now, ↴

From the numbers 1 to 10 (2, 3, 5, 7) are the prime numbers because they are just divisible by itself and 1 only.

Till here We have founded that there are 4 Prime numbers from 1 to10.

Now, We have to find the of probability of the event that a number chosen from 1 to 10 is a prime numbers.

Formula of finding Probability is : ↴

$\boxed {\mathrm { \frac{Number \: of \: Favourable \: outcomes. }{Total \: numbers \: of \: outcomes. } }}$

Here the total outcomes are 10 and the favourable outcomes are 4.

So, According to the formula : ↴

$\sf \: Probability \: of \: prime \: numbers \: chosen \: from \: 1 \: to \: 10 \: is \: : \: \cfrac{4}{10}$

$\sf \: Now \: we \: will \: convert \: \cfrac{4}{10} \: into \: simplest \: form \: : \:$

$\sf \: \cfrac{4}{10} \: \longrightarrow \: \cfrac{ \cancel4}{ \cancel{10}} \: = \cfrac{2}{5}$