12.02 Venn diagrams and two-way tables

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?

Rosey wants to decide which movie to watch from a streaming website. A Venn diagram of her options sorts movies into three categories based on their genre:

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?

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

a

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

b

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

c

Danielle is told that her partner will be randomly assigned. What is the probability that her partner will be suitable?

David makes a Venn diagram about the possible pets he could get from the local shelter. He is told that his new pet will be selected at random.

a

What is the probability that his new pet will be a dog that isn't fluffy?

b

What is the probability that his new pet won't be fluffy?

c

What is the probability that his new pet will be fluffy?

Bill 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 the movies into three categories:

Comedic films, romantic films, and runtime over 2 hours.

a

How many movies are there in Bill's collection?

b

Bill wants to watch a comedy. What is the probability he will select a comedy?

c

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

d

Bill is after a comedy film that goes for longer than 2 hours. What is the probability that he will select a suitable film?

The results from a recent survey showed that 56 people speak Spanish or French. Of these, 36 speak Spanish, and 18 speak both Spanish and French. Find the number of people surveyed who speak French.

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 teacher 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.

Miss Merryweather recorded the hair colour and hair type of her students in the following graph:

Complete the following two-way table from the information in the graph:

38 students were asked whether or not they were allergic to nuts and dairy. Data is recorded in the following two-way table:

A healthy living initiative asked people to describe how often they go to the gym. The table below summarizes the result:

A group of tourists were asked whether they spoke Mandarin or Spanish. The result is summarized in the table below:

In a study, some people were asked whether they were vegetarian or not. 27 responders said they were vegetarian, of which 8 were children. 18 children said they were not vegetarian, and 21 adults said they are not vegetarians.

In a study, some people were asked whether they lie. A partially completed two-way table of the results is shown below:

The following table describes the departures of trains out of a train station for the months of March and April:

A student makes a Venn diagram of students who are late to school, and students who catch the bus to school.

Using the Venn diagram, complete the following table:

	Late	Not late
Caught bus
Didn't catch bus

60 residents of a city were asked "Do you support the construction of the new train station?". The residents questioned were also classified as living in the North, South or in the inner city.

Using the Venn diagram, complete the following table:

	North	South	Inner
Yes
No

Students in Xanthe's class were asked if they owned a dog and asked if they owned a snake. The following two-way table shows the results of the survey:

Construct a Venn diagram that represents the information provided in the two-way table.

A vet has 25 pets visit their practice in a day. The pets are categorised based on whether they have been vaccinated and whether they have been microchipped.

Using the Venn diagram, complete the following table:

	Microchipped	Not Microchipped
Vaccinated
Not vaccinated

Vanessa wants to sort a list of 11 numbers based on whether they contain a 3, and whether they are even. The list of terms is shown below:

1, \, 2, \, 3, \, 5, \, 8, \, 13, \, 21, \, 34, \, 55, \, 89, \, 144

If a term from the list is chosen at random, find the probability that it:

In a particular class, 5 people play both football and tennis, 13 people in total play tennis, and 11 in total play football.

In a study, a number of people were asked whether they were musicians or not. 29 responders said they were a musician, of which 8 were children. 19 children said they were not musicians, and 12 adults said they are not musicians.

A group of 132 students are to choose to study either Mandarin or Spanish (or both). 67 students choose Mandarin and 72 students choose Spanish.

A student is making a Venn diagram about politicians in the last two elections. Looking at a group of 24 politicians, 14 ran in the first election and 19 ran in the second election.

A small magazine asked people from different states to send in a vote on whether they supported Daylight Saving Time, the results are shown in the following figure:

a

What proportion of people voted "YES"?

b

What proportion of "NO" votes are from NSW?

c

Considering just the voters from NSW and ACT, what proportion of the votes are NSW "YES" votes?

In a group of 190 primary and senior students, 88 are primary students. The students fell into three categories of travel to school - by bus, car, or walking. 109 students get to school by bus, of which 52 are primary students. 50 students get to school by car, of which 20 are primary students

The employees of Koala Airlines were discussing where they should hold their end of year party. Of all of the employees:

• 53 would go to a restaurant
• 67 would go to a bowling alley
• 76 would go to a theme park
• 16 would only go to either a restaurant or a bowling alley
• 29 would only go to either a bowling alley or the theme park
• 17 would only go to either a restaurant or the theme park
• 4 would not go to a restaurant or a bowling alley or to the theme park
• 5 would go to all three places