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

Mathematics

2 answers:

BARSIC [14]3 years ago

6 0

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%.

Brilliant_brown [7]3 years ago

3 0

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.

You might be interested in

Y – 1 = 2(x – 2), solve for y

solmaris [256]

Answer:

y = 2x-3

Step-by-step explanation:

y – 1 = 2(x – 2)

Distribute

y-1 =2x-4

Add 1 to each side

y-1+1 = 2x-4+1

y = 2x-3

6 0

2 years ago

Find the population mean or sample mean as indicated. Sample: 19, 15, 6, 11, 24 Compute the sample mean for this data set. Selec

yKpoI14uk [10]

Answer:

$\overline{x}=15$

Step-by-step explanation:

the mean is given by:

$\overline{x} = \dfrac{\sum\limits_{i=1}^n x_i}{n} \quad\text{or}\quad \dfrac{\text{sum of all items}}{\text{number of items}}$

In our case this is:

$\overline{x} = \dfrac{19+15+6+11+24}{5} \Rightarrow \dfrac{75}{5}\\\\\overline{x} = 15\\\\$

side note: the main difference between sample mean and population mean is in the 'context'. However, the method to calculate them is the same.

By context I mean: if this the items are taken from some larger category for example: the ages of a few 'students' from a 'class'. Here 'students' are the sample from a larger set that is 'class'. The mean of the 'few students' will be called sample mean. In contrast, if we take the mean of the ages of the whole class then this is called population mean. (population mean == mean of the whole set)

In our case we aren't told exactly where these numbers come from, is this the whole set or a sample from it, the lack of context allows us to assume that the mean can either be population mean or sample mean. So we can safely use any symbol $\mu$ or $\overline{x}$ .