### Video Transcript

If a number is selected at random
from one to 30, what is the probability of selecting a prime number?

Let’s begin by recalling what we
mean by a prime number. A prime number is an integer which
has exactly two factors, one and itself. For this reason, one is not
actually a prime number since it only has one factor. Let’s list out the rest of the
numbers between one and 30 and find the ones that are prime.

Two is the only even prime number
since its factors are one and two. The next three prime numbers are
three, five, and seven. Nine is not a prime since it has
factors of one and nine, but also three. 11, 13, 17, and 19 are the next
four. A common mistake is to think that
21 is a prime number. However, the factors of 21 are one
and 21, but also three and seven. In fact, the only prime numbers
between 20 and 30 are 23 and 29. There’s a total of 10 prime numbers
in that list.

Now remember, the probability of an
event occurring is found by calculating the number of ways for the event to occur
and dividing it by the total number of outcomes. For this question, we’re dividing
the total number of prime numbers by the total amount of numbers all together. That’s 10 divided by 30. We can simplify this fraction by
dividing both the numerator and the denominator by 10. And we get that the probability of
selecting a prime number is one-third.