Question 1

Based on the first Venn diagram, how many members attend both Yoga and Zumba classes?

Accepted Answer

$$34$$

Question 2

Using the first Venn diagram, how many members attend only Yoga classes?

Accepted Answer

$$54$$

Question 3

According to the first Venn diagram, how many members do not attend either Yoga or Zumba?

Accepted Answer

$$31$$

Question 4

How many total members were surveyed in the first Venn diagram?

Accepted Answer

$$54 + 34 + 31 = 119$$, but including those outside both: $$54 + 34 + 31 + 31 = 150$$

Question 5

In the second Venn diagram, how many students use all three study methods (flashcards, study groups, and tutoring)?

Accepted Answer

$$10$$

Question 6

According to the second Venn diagram, how many students use only flashcards?

Accepted Answer

$$39$$

Question 7

How many students use both flashcards and study groups, but not tutoring, according to the second Venn diagram?

Accepted Answer

$$25$$

Question 8

How many students use at least two study methods in the second Venn diagram?

Accepted Answer

$$25 + 10 + 12 = 47 ($$students using at least two methods)

Question 9

How many students do not use any of the three study methods in the second Venn diagram?

Accepted Answer

$$31$$

Question 10

If a student is selected at random from the group in the second Venn diagram, what is the probability that the student uses exactly one study method?

Accepted Answer

$$\frac{39 + 27 + 18}{180}$$

Question 11

A survey of 150 students found that 95 read fiction, 70 read non-fiction, and 32 read both. How many students read only fiction?

Accepted Answer

$$95 - 32 = 63$$

Question 12

A marketing firm surveyed 320 business owners: 185 used social media, 142 used email marketing, and 76 used both. How many used only email marketing?

Accepted Answer

$$142 - 76 = 66$$

Question 13

A retail store tracked 200 customers: 90 bought jackets, 75 bought sneakers, 60 bought backpacks, 30 bought jackets and sneakers, 25 bought jackets and backpacks, 20 bought sneakers and backpacks, and 12 bought all three. How many bought only jackets?

Accepted Answer

$$90 - 30 - 25 + 12 = 47$$

Question 14

In a survey, 54 people attend only Yoga, 31 attend only Zumba, 34 attend both, and 31 attend neither. What is the probability that a randomly selected person attends at least one class?

Accepted Answer

$$\frac{54 + 31 + 34}{150}$$

Question 15

Given the Venn diagram for Yoga and Zumba, how many people attend exactly one of the two classes?

Accepted Answer

$$54 + 31 = 85$$

Question 16

If a student is selected at random from the group in the second Venn diagram, what is the probability that the student uses at least two study methods?

Accepted Answer

$$\frac{25 + 10 + 12}{180}$$

Question 17

A survey of 150 students found that 95 read fiction, 70 read non-fiction, and 32 read both. How many students read neither fiction nor non-fiction?

Accepted Answer

$$150 - (95 + 70 - 32) = 17$$

Set Applications: Survey Problems and Venn Diagrams

Study Guide - Practice Questions

Study Guide - Flashcards