Question

What percent of the first 20 natural numbers are prime numbers?

Answer 1

Answer:  The required percentage is 40%.

Step-by-step explanation:  We are given to find the percentage of the first 20 natural numbers that are prime.

We know that

first 20 natural numbers are 1, 2, 3, 4,  .  .  .  , 19, 20.

And, the prime numbers among them are 2, 3, 5, 7, 11, 13, 17 and 19.

So, if S be the sample space for the experiment and A be the event of selecting a prime number.

Then, we have

n(S) = 20  and  n(A) = 8.

Therefore, the probability of event A is given by

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{8}{20}=\dfrac{2}{5}\times100\%=40\%.$

Thus, the required percentage is 40%.  

Answer 2

The primes are 2, 3, 5, 7, 11, 13, 17, 19. There are 8 of them, so they make up 40% of the numbers 1–20.