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.
