Question

What is the probability that a number picked from the first twenty natural numbers is an even composite number?

Answer 1

Hint : Write down the even composite numbers from the first twenty natural numbers.

Composite numbers can be defined as the whole numbers that have more than two factors.
Whole numbers that are not prime are composite numbers (except 1).

We have to find the probability of picking an even composite number from the first 20 natural numbers.
Even composite numbers from first 20 natural numbers $ = 4, 6, 8, 10, 12, 14, 16, 18, 20$
Hence the number of even composite numbers from the first 20 natural numbers is 9.
Let E be an event of picking up even composite number so $n(E) = 9$
Total numbers that we need to pick from equal to 20 as given in the question statement.
So $n(S) = 20$
Hence \[P(E) = \dfrac{{n(E)}}{{n(S)}} = \dfrac{9}{{20}}\]

Note: Whenever we come across such problems some knowledge of number systems is needed. Whole numbers that are not prime are composite numbers (except 1). In these types of problems we have to find the number of elements in sample space and the required event to find the probability.