# Question Video: Determining the Probability of an Event Mathematics

What is the probability of selecting at random a prime number from the numbers 8, 9, 20, 19, 3, and 15?

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### Video Transcript

What is the probability of selecting at random a prime number from the numbers eight, nine, 20, 19, three, and 15?

In order to answer this question, we’ll need to recall two things, firstly, how we find the probability of an event, and, secondly, what a prime number is. In order to calculate the probability, then we can use the formula to calculate the probability of an event 𝐴 as the number of elements in event 𝐴 divided by the number of elements in a sample space 𝑆. We may also see this formula written as the probability of an event is equal to the number of favorable outcomes over the total number of outcomes. Here, we’re trying to calculate the probability of selecting a prime number. A prime number is a number that has exactly two factors, one and itself.

So let’s consider the list of numbers that we were given. The first three values eight, nine, and 20 are not prime because they have more than two factors. Next, 19 and three are both prime numbers. However, 15 is not a prime number. When it comes to using the formula then, the number of prime numbers that we have is two. That’s three and 19. The value on the denominator will be six, since there were six numbers in total. It’s always good to simplify our fractions where we can. And so we can give the answer that the probability of selecting a prime number from the given list of numbers is one-third.