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# Question Video: Calculating the Experimental Probability of an Event Using a Frequency Table Mathematics

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

02:09

### Video Transcript

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

We can begin this question by having a look at the table. We can see that out of 20 students, 10 students said that eggs were their favorite breakfast, two students said that cereal was, and eight students said that toast was their favorite. When it comes to calculating the probability that a student prefers eggs, we’re really considering this as experimental probability. Although it doesn’t appear to be a traditional experiment, there has been a repeated trial of asking different students for their favorite breakfast and then a recording of the outcomes. That’s the answers that the students gave. The standard formula that we might use to calculate experimental probability can be given that this is equal to the number of trials in which the outcome occurs over the total number of trials.

However, we can rewrite this according to the context. We want to calculate the probability that a student prefers eggs. So that can be calculated as the number of students who preferred eggs over the total number of students surveyed. Then, from the table, we can see that there were a total of 10 students who preferred eggs. And we are told that 20 students were surveyed in total. Notice that even if we weren’t given the figure of 20, we could calculate this from the sum of the frequencies, that’s the number of students, of 10 plus two plus eight. So we now have that the probability of a student preferring eggs is 10 over 20. But of course we know that this fraction can be simplified further to one-half. And so we can give the answer that the probability that a randomly selected student prefers eggs is one-half.

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