# Video: Determining the Probability of an Event

The table shows the results of a survey that asked 20 students about their favourite breakfast. What is the probability that a randomly selected student prefers eggs?

01:20

### Video Transcript

The table shows the results of a survey that asked 20 students about their favourite breakfast. What is the probability that a randomly selected student prefers eggs?

In this question, to calculate the probability, we’re going to work out the experimental probability, which is also referred to as relative frequency. We can use the calculation that the relative frequency of an event E is equal to the number of times E occurs divided by the total number of trials. So, for this question, to find the probability that a student prefers eggs, this is equivalent to finding the relative frequency of a student who prefers eggs and will be equal to the number of students who prefer eggs over the total number of students.

We then use the table to establish that there are 10 students who prefer eggs and 20 students in total. Even if we hadn’t been given that the 20 students were asked, we could’ve calculated this value by adding up the values of 10, two, and eight in the table. We can then simplify our fraction 10 over 20 as one-half. So, our final answer as a decimal for the probability that a randomly selected student prefers eggs is 0.5. In this case, our fractions 10 over 20, one-half, and the decimal 0.5 would all be equally valid answers for the probability.