Question

In an AP* Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. What is the probability that a student from this class eats breakfast but does not floss their teeth

Answer 1

The probability that a student from this class eats breakfast but does not floss their teeth is .11 (11%).

Explanation:

Let's start by making a two-way table (you can also make a tree diagram).

Let's make the total number of students = 100. Now, fill out the table using the given probabilities from the question.

We are given that 57% of students eat breakfast in the morning, so the total in the "Eats breakfast" column is 57.

80% of the students floss their teeth, so the total in the "Flosses teeth" row is 80.

We can fill out the rest of the table using simple algebra and the fact that the probabilities must add up to 1.

I've attached a table that I created showing what the two-way table should look like when filled out completely.

Now, we want to find the probability that a student eats breakfast but does not floss their teeth.

We can look at the column "Eats breakfast" and the row "Does not floss teeth" and see that 11 (out of 100) students eat breakfast without flossing their teeth.

Therefore, the probability that a student from this class eats breakfast without flossing their teeth is .11.