Question

What is the probability of a number picked from the first nineteen natural numbers is an even composite number?

Answer 1

Hint:
$\bullet$ Probability is the term mathematically with events that occur, which is the number of favorable events that divides the total number of the outcomes.
$\bullet$ If we divide the probability and then multiplied with the hundred then we will determine its percentage value.
$\bullet$ $\dfrac{1}{6}$ which means the favorable event is $1$ and the total outcome is $6$
Formula used:
$\bullet$ $P = \dfrac{F}{T}$where P is the overall probability, F is the possible favorable events and T is the total outcomes from the given.

Complete step-by-step solution:
First, we will need to know about the prime numbers and composite numbers.
$\bullet$ Prime numbers are the numbers that are divisible by themselves and $1$ only or also known as the numbers whose factors are the given number itself.
$\bullet$ But the composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself)
$\bullet$ Every composite number can be represented in the form of prime factorization.
Also, the natural numbers are represented as $1,2,3,4,.....\infty $
Since the first nineteen natural numbers are even composite numbers. This means it should be an even number and also the composite number.
First, we will describe the prime numbers on the first nineteen, which are $2,3,5,7,11,13,17,19$
Thus, we get the composite numbers as $4,6,8,10,12,14,16,18$ which are composites and also even numbers.
Hence the favorable event is $4,6,8,10,12,14,16,18$ in total we get $8$
And the total event is $1,2,3,...,19$ in total we have $19$
Therefore, the probability of the first twenty natural numbers being an even composite number is $P = \dfrac{F}{T} \Rightarrow \dfrac{8}{{19}}$.

Note: We can find whether the given number is prime or composite by the trial-and-error methods. Divide the number from the prime numbers less than the given number. if the number is exactly divisible by the prime number, it is the composite number, if not then it is the prime number.
The only even prime number is $2$ and all other prime numbers are odd.