Exercise 31 Page 798

Practice makes perfect

a Let's look at the given Venn diagram.

To know how many students are in the senior class, we will add all the sections in the diagram.

67 + 10 + 30 + 8 + 4 + 38 + 51 + 137 = 345

b To know how many students participate in athletics, we will add every section of the athletics circle in the Venn diagram.

Let's do it!

137 + 8 + 10 + 4 = 159

c We can see in the Venn diagram that athletics and drama are not mutually exclusive events. Let's recall how to find the probability of two events,

A

and

B,

that are not mutually exclusive.

P (A or B) = P (A) + P (B) - P (A and B)

To find the probability of a student participating in athletics, we will divide the number of students in athletics that we found in Part B by the total students in the senior class that we found in Part A.

P (athletics) = \frac{1 5 9}{3 4 5}

Let's find out how many students participate in drama by adding the number in every section of the drama circle in the Venn diagram.

Let's do it!

38 + 30 + 10 + 4 = 82

Now, to find the probability of a student participating in drama, we will divide the number of students in drama by the total amount of students.

P (drama) = \frac{8 2}{3 4 5}

We will add the sections that both drama and athletics share in the diagram.

Let's do it!

4 + 10 = 14

To find the probability of a student participating in both athletics and drama, we will divide the students that participate in both activities by the total amount of students.