Middle Years

# 12.03 Venn diagrams

Worksheet
Venn diagrams
1

A group of students were asked why they skipped breakfast. The two reasons given were that they were "not hungry" and they were "too busy".

a

How many of the students skipped breakfast because they were not hungry?

b

How many of the students only skipped breakfast because they were too busy?

c

How many of the students skipped breakfast because of one reason?

2

A group of students were asked about their siblings. The two categories show if they have at least one brother, and if they have at least one sister:

a

How many of the students have at least one sibling?

b

How many of the students have at least one brother?

c

How many of the students don't have a sister?

3

A jeweller has arranged his gems based on the cut and colour of the gem:

• Cuts - triangular, rectangular, and octagonal
• Colours - amethysts, emeralds, and rubies
a

How many of the gems are rubies?

b

How many of the gems are triangular?

c

How many of the gems are both rubies and triangular?

4

A jeweller has arranged his gems based on the cut and colour of the gem:

• Cuts - triangular, rectangular, and octagonal
• Colours - amethysts, emeralds, and rubies
a

How many of the gems are not rubies?

b

How many of the gems are both ruby and triangular?

c

How many of the gems are rubies that aren't triangular?

5

A jeweller has arranged his gems based on the cut and colour of the gem:

• Cuts - triangular, rectangular, and octagonal

• Colours - amethysts, emeralds, and rubies

Write an appropriate category name for "Circle 2" in the diagram.

6

A student is arranging a list of seven numbers into two categories. One category is his lucky numbers.

Write an appropriate category name for "Circle 1" in the diagram.

7

A student creates the following diagram of their favourite animals:

a

How many of the animals have four legs?

b

How many of the animals have four legs and stripes?

c

How many of the animals have four legs or stripes, but not both?

8

The following diagram is used for sorting numbers according to two categories:

• Numbers that are divisible by 7
• Numbers that are even
a

Construct a Venn diagram and shade the area where you would place the 8.

b

Construct a Venn diagram and shade the area where you would place the 14.

c

Construct a Venn diagram and shade the area where you would place the 15.

9

The Venn diagram shows the overlap of students who own a pet and students who own a bicycle:

a

Construct a Venn diagram and shade the area that represents the students who own a pet and own a bicycle.

b

Construct a Venn diagram and shade the area that represents the students who own a pet but don't own a bicycle.

10

A student is making a Venn diagram from the information gathered from her classmates: 18 people play cricket, 15 play softball, and 6 play both softball and cricket.

a

How many people only play softball?

b

Construct a Venn diagram that shows how many students play each sport.

11

A student is making a Venn diagram about a recent catch-up test for those that missed or did poorly on the original test. In the class of 30 students, 27 did the original test and 10 did the catch-up test.

a

Given that everyone in the class did at least one test, how many people did both tests?

b

Construct a Venn diagram that shows how many students did each test.

12

Avril makes a Venn diagram about the possible dance partners in her dance class:

a

How many students are there in Avril's class, not including Avril?

b

Avril thinks her partner is suitable if they are both good dancers and the right height for her. How many suitable partners are there in the class?

c

Avril is told that her partner will be randomly assigned. Find the probability that her partner will be suitable.

13

Carl makes a Venn diagram about the possible pets he could get from the local shelter:

a

Carl is told that a pet will be selected at random. Find the probability that his new pet will be a dog that isn't fluffy.

b

Carl is told that a pet will be selected at random. Find the probability that his new pet won't be fluffy.

14

The given Venn diagram shows the number of students in a school playing rugby league, rugby union, both or neither:

Find the number of students who:

a

Play rugby league only.

b

Play rugby league.

c

Play rugby union.

d

Play rugby union only.

e

Do not play rugby league.

f

Do not play rugby union.

15

The diagram shows the decisions of 448 workers choosing to work and workers choosing to strike on a particular day of industrial action.

Find the number of workers who chose to:

a

Strike.

b

Strike and work.

c

Work and not strike.

d

Work or strike.

e
Neither work nor strike.
16

The Venn diagram shows the number of students choosing to study on the night before an exam, and the number of students choosing to party:

Find the number of students that chose:

a

To party.

b

Not to study.

c

Neither to study nor party.

17

The Venn diagram shows the decisions of 535 consumers choosing to buy an iPhone and consumers choosing to buy a Blackberry.

Find the number of consumers that chose to buy:

a

A Blackberry.

b

A Blackberry only.

c

Both phones.

d

An iPhone or a Blackberry.

e

Neither phones.

f

An iPhone but not a Blackberry.

Three circle Venn diagrams
18

Joanne is struggling to decide what to watch online. She decides to pick one movie at random from the streaming website. A Venn diagram of her options sorts movies into three categories based on their genre: Comedy, Action and Horror:

a

How many of the movies are horror films?

b

How many of the movies fit into only one genre?

c

How many of the movies are an action film combined with at least one other genre?

19

Charlie is struggling to decide what movie to watch. He decides to pick one at random from his collection. A Venn diagram of his collection sorts movies into three categories: Comedic films; Romantic films, and runtime is over 2 hours:

a

How many movies are there in Charlie's collection?

b

Charlie wants to watch a comedy. Find the probability he will select a a comedy.

c

Charlie is after a romantic comedy that goes for less than 2 hours. Find the probability that he will select a suitable film.

d

Charlie is after a comedy film that goes for longer than 2 hours. Find the probability that he will select a suitable film.

20

A florist collected a sample of her flowers and divided them into the appropriate categories as shown in the Venn diagram:

Find the number of flowers which are:

a

Not red but have thorns.

b

Not red and does not have thorns.

21

The Venn diagram shows the overlap of students who play netball, soccer and rowing.

a

Construct a Venn diagram and shade the area that represents the students who play two or more sports.

b

Construct a Venn diagram and shade the area that represents the students who row but don't play netball.

22

The following diagram is used for sorting shapes according to three categories:

• Shapes with exactly three sides

• Shapes with at least one right angle
• Shapes with sides that are all equal in length
a

Construct a Venn diagram and shade the area where you would place "a rectangle that isn't a square".

b

Construct a Venn diagram and shade the area where you would place "an equilateral triangle".

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