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Middle Years

12.04 Two-way tables

Worksheet
Two-way tables
1

50 students were asked whether or not they were allergic to nuts and dairy. The two-way table is provided below:

Allergic to NutsNot Allergic to Nuts
Allergic to Dairy 6 11
Not Allergic to Dairy 6 27
a

How many students are allergic to nuts?

b

How many students are allergic to nuts or dairy, or both?

c

How many students are allergic to at most one of the two things?

2

Some students were asked if they are left or right handed. The results are provided in the following table:

A student is picked from this group at random.

a

How many of the students are right-handed males?

b

How many of the students are left-handed?

c

How many of the students are not right-handed males?

Left-handedRight-handedTotal
Female 10 39 49
Male 5 50 55
Total 15 89 104
3

Mr. Tobit asked the students in his class to pick their favourite subject. He displayed the results in the following two-way table:

a

How many girls did not pick maths as their favourite subject?

b

How many students picked music?

c

How many boys are in Mr. Tobit's class?

BoysGirls
Maths1112
Music818
Science1311
English1510
4

170 tennis players were asked whether they would support equal prize money for the women’s and men’s draw.

Complete the following table:

SupportDo not support
Males 35
Females 71 15
5

A healthy living initiative asked people to describe how often they go to the gym. Their responses are shown in the following table:

a

How many people were surveyed?

b

If one person is chosen at random, find the exact probability that they are a male who frequently attends the gym.

c

If one person is chosen at random, find the probability that they attend the gym rarely.

FemaleMale
Frequently3537
Rarely3513
6

Members of a gym were asked what kind of training they do. The two way table shows the results:

a

How many gym members were asked altogether?

b

How many members do weight training?

c

If a member is chosen at random, what is the probability that they do weight training?

d

According to the table which is more likely doing weight training, men or women?

CardioWeight
Male1130
Female4712
7

A nonsmoking initiative asked smokers to describe how often they smoke:

a

How many people were surveyed?

b

If one person is chosen at random, what is the probability that they are a frequent male smoker?

c

If one person is chosen at random, what is the probability that they smoke rarely?

FemaleMale
Frequently5734
Rarely3514
8

A town has two campsites to choose between which both offer tent and cabin accomodation. This two-way table records the campers choices in one summer:

TentCabin
Sunny Campground 178 62
Platypus Creek 101 281
a

How many people stayed in one of the town's campsite?

b

State the proportion of the people that stayed in a tent.

c

State the proportion of the people who stayed in cabins was in Sunny Campground. .

d

State the proportion of people stayed at Platypus Creek.

9

A group of tourists were asked whether they spoke Mandarin or Spanish.

a

Complete the following table:

b

How many people speak both languages?

c

If one person is chosen at random, find the probability that they speak neither language.

d

If one person is chosen at random, find the probability that they speak only one of the languages.

SpanishNot SpanishTotal
Mandarin 58 10
Not Mandarin 15 17
10

Sophia asked some people in her community whether they were vegetarian or not. 29 responders said they were vegetarian, of which 8 were children. 14 children said they were not vegetarian, and 11 adults said they are not vegetarians.

a

Construct a two-way table based on the results of Sophia's survey.

b

State the proportion of responders that are vegetarian.

c

State the proportion of adults that are vegetarian.

11

The following table shows the number of trains arriving either on time or late at a particular station:

a

How many trains were late on Friday?

b

How many trains passed through the station on Wednesday?

c

How many trains were on time throughout the entire week?

d

State the proportion of trains that were on time over the whole week. .

\text{Arrived} \\ \text{on time}\text{Arrived} \\ \text{late}
Monday23 9
Tuesday20 5
Wednesday27 8
Thursday2814
Friday1512
Saturday22 6
Sunday2613
12

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

a

Complete the following table:

b

Of those in the study, one is chosen at random. Find the probability that they said they never lie.

LieDont LieTotal
Children 15 25
Adults 10
Total 60
13

This table describes the departures of trains out of a train station for the months of May and June:

Departed on timeDelayed
\text{May}123 32
\text{June}124 47
a

How many trains departed during May and June?

b

State the proportion of the trains in June that were delayed. Write your answer as a percentage to one decimal place.

c

State the proportion of the total number of trains during the 2 months that were ones that departed on time in May. Give your answer as a percentage rounded to one decimal place.

d

Find the probability that a train selected at random in June would have departed on time. .

e

Find the probability that a train selected at random from the 2 months was delayed.

14

At a local university, students were asked what their favourite subject at high school was and what they have decided to major in after 3 years of university. The results are shown in the following table:

Maths favouriteScience favouriteMusic favouriteArt favouriteTotal
Maths major 7620 61 43200
Science major 6446 53 59222
Music major 6411 67 59201
Art major 619 38 74137
Total 21096 219 235760

One student is chosen at random. Find:

a

The probability that a student's favourite subject was mathematics at high school.

b

The probability that a student is majoring in music or arts at university.

c

The probability that a student's favourite subject was music and they studied something different at university.

d

The probability that a student's major is the same as their favourite subject?

Two-way tables and Venn diagrams
15

Consider the Venn diagram:

Complete the table of values below.

Play Rugby LeagueDon't play Rugby League
Play Rugby Union
Don't play Rugby Union
16

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

Construct a two-way table based on the Venn diagram.

17

A vet has 28 pets visit their practice in a day. The pets are categorised based on whether they have been vaccinated and whether they have been microchipped.

Construct a two-way table based on the Venn diagram.

18

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.

Construct a two-way table based on the Venn diagram.

19

Students in Irene's class were asked if they owned a dog and asked if they owned a snake. The following two-way table shows that information:

Owns a dogDoesn't own a dog
Owns a snake 2 3
Doesn't own a snake 13 11

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

20

100 random people in Australia were surveyed, examining their carbon footprint and the city they lived in. The people were then categorised as living in either an urban or regional location, and whether that person has a high carbon emission or low carbon emission.

UrbanRegionalTotal
High Emission37 13 50
Low Emission24 26 50
Total61 39 100

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

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