50 students were asked whether or not they were allergic to nuts and dairy. The two-way table is provided below:
| Allergic to Nuts | Not Allergic to Nuts | |
|---|---|---|
| Allergic to Dairy | 6 | 11 |
| Not Allergic to Dairy | 6 | 27 |
How many students are allergic to nuts?
How many students are allergic to nuts or dairy, or both?
How many students are allergic to at most one of the two things?
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.
How many of the students are right-handed males?
How many of the students are left-handed?
How many of the students are not right-handed males?
| Left-handed | Right-handed | Total | |
|---|---|---|---|
| Female | 10 | 39 | 49 |
| Male | 5 | 50 | 55 |
| Total | 15 | 89 | 104 |
Mr. Tobit asked the students in his class to pick their favourite subject. He displayed the results in the following two-way table:
How many girls did not pick maths as their favourite subject?
How many students picked music?
How many boys are in Mr. Tobit's class?
| Boys | Girls | |
|---|---|---|
| Maths | 11 | 12 |
| Music | 8 | 18 |
| Science | 13 | 11 |
| English | 15 | 10 |
170 tennis players were asked whether they would support equal prize money for the women’s and men’s draw.
Explain how to find the missing value in the table.
| Support | Do not support | |
|---|---|---|
| Males | 35 | |
| Females | 71 | 15 |
A healthy living initiative asked people to describe how often they go to the gym. Their responses are shown in the following table:
How many people were surveyed?
If one person is chosen at random, find the exact probability that they are a male who frequently attends the gym.
If one person is chosen at random, find the probability that they attend the gym rarely.
| Female | Male | |
|---|---|---|
| Frequently | 35 | 37 |
| Rarely | 35 | 13 |
Members of a gym were asked what kind of training they do. The two way table shows the results:
How many gym members were asked altogether?
How many members do weight training?
If a member is chosen at random, what is the probability that they do weight training?
According to the table which is more likely doing weight training, men or women?
| Cardio | Weight | |
|---|---|---|
| Male | 11 | 30 |
| Female | 47 | 12 |
A nonsmoking initiative asked smokers to describe how often they smoke:
How many people were surveyed?
If one person is chosen at random, what is the probability that they are a frequent male smoker?
If one person is chosen at random, what is the probability that they smoke rarely?
| Female | Male | |
|---|---|---|
| Frequently | 57 | 34 |
| Rarely | 35 | 14 |
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:
| Tent | Cabin | |
|---|---|---|
| Sunny Campground | 178 | 62 |
| Platypus Creek | 101 | 281 |
How many people stayed in one of the town's campsite?
State the proportion of the people that stayed in a tent.
State the proportion of the people who stayed in cabins was in Sunny Campground. .
State the proportion of people stayed at Platypus Creek.
A group of tourists were asked whether they spoke Mandarin or Spanish.
Complete the following table:
How many people speak both languages?
If one person is chosen at random, find the probability that they speak neither language.
If one person is chosen at random, find the probability that they speak only one of the languages.
| Spanish | Not Spanish | Total | |
|---|---|---|---|
| Mandarin | 58 | 10 | |
| Not Mandarin | 15 | 17 |
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.
Construct a two-way table based on the results of Sophia's survey.
State the proportion of responders that are vegetarian.
State the proportion of adults that are vegetarian.
The following table shows the number of trains arriving either on time or late at a particular station:
How many trains were late on Friday?
How many trains passed through the station on Wednesday?
How many trains were on time throughout the entire week?
State the proportion of trains that were on time over the whole week. .
| \text{Arrived} \\ \text{on time} | \text{Arrived} \\ \text{late} | |
|---|---|---|
| Monday | 23 | 9 |
| Tuesday | 20 | 5 |
| Wednesday | 27 | 8 |
| Thursday | 28 | 14 |
| Friday | 15 | 12 |
| Saturday | 22 | 6 |
| Sunday | 26 | 13 |
In a study, some people were asked whether they lie. A partially completed two-way table of the results is shown below.
Complete the following table:
Of those in the study, one is chosen at random. Find the probability that they said they never lie.
| Lie | Dont Lie | Total | |
|---|---|---|---|
| Children | 15 | 25 | |
| Adults | 10 | ||
| Total | 60 |
This table describes the departures of trains out of a train station for the months of May and June:
| Departed on time | Delayed | |
|---|---|---|
| \text{May} | 123 | 32 |
| \text{June} | 124 | 47 |
How many trains departed during May and June?
State the proportion of the trains in June that were delayed. Write your answer as a percentage to one decimal place.
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.
Find the probability that a train selected at random in June would have departed on time.
Find the probability that a train selected at random from the 2 months was delayed.
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 favourite | Science favourite | Music favourite | Art favourite | Total | |
|---|---|---|---|---|---|
| Maths major | 76 | 20 | 61 | 43 | 200 |
| Science major | 64 | 46 | 53 | 59 | 222 |
| Music major | 64 | 11 | 67 | 59 | 201 |
| Art major | 6 | 19 | 38 | 74 | 137 |
| Total | 210 | 96 | 219 | 235 | 760 |
One student is chosen at random. Find:
The probability that a student's favourite subject was mathematics at high school.
The probability that a student is majoring in music or arts at university.
The probability that a student's favourite subject was music and they studied something different at university.
The probability that a student's major is the same as their favourite subject?
Consider the Venn diagram:
Complete the table of values below.
| Play Rugby League | Don't play Rugby League | |
|---|---|---|
| Play Rugby Union | ||
| Don't play Rugby Union |
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.
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.
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.
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 dog | Doesn'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.
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.
| Urban | Regional | Total | |
|---|---|---|---|
| High Emission | 37 | 13 | 50 |
| Low Emission | 24 | 26 | 50 |
| Total | 61 | 39 | 100 |
Construct a Venn diagram that represents the information provided in the two-way table.
In a class, 5 students play both football and tennis, 13 students in total play tennis, and 11 in total play football.
How many students only play football?
How many students play only one sport?
If a random student is chosen from the group, find the probability that the student only plays tennis.
Consider the following list of numbers: 1,2, \, 3, \, 5, \, 8, \, 13, \, 21, \, 34, \, 55, \, 89, \, 144
If a number from the list is chosen at random, find:
The probability that it is an even number that doesn't contain a 3.
The probability that it contains a 3 or is an odd number.
The probability that it is either odd or contains a 3, but not both.
A grade of 234 students are to choose to study either Mandarin or Spanish (or both). 134 students choose Mandarin and 120 students choose Spanish.
How many students have chosen both languages?
If a student is picked at random, find the probability that the student has chosen Spanish only.
If a student is picked at random, find the probability that the student has not chosen Mandarin.
In a music school of 129 students, 83 students play the piano, 80 students play the guitar and 14 students play neither. Find the probability that a student chosen at random plays:
Both the piano and the guitar.
The piano or the guitar.
Neither the piano nor the guitar.
In a survey of 31 students, it was found that 16 students play tennis and 14 students play hockey. 2 students play none of these sports, 8 play both tennis and cricket, 7 play both cricket and hockey, 6 play both tennis and hockey and 3 play all three.
Find the probability that a randomly selected student plays all three sports.
In a study, some people were asked whether they were musicians or not. 25 responders said they were a musician, of which 10 were children. 25 children said they were not musicians, and 13 adults said they are not musicians.
How many people were in the study?
State the proportion of responders that are musicians.
State the proportion of adults that are musicians.
In a particular high school where there are 91 year 8 students, 40 students study History only, 36 students study French only and 10 students study both. If a student is randomly chosen, find the probability that this student is studying:
History and French.
History only.
French only.
French or History.
Neither subject.
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.
Given that every politician examined was in at least one election, how many politicians ran in both elections?
If a politician is randomly chosen in the second election, find the probability they were also in the first election.
In a survey, 104 students were asked if they are left or right-handed, of which 49 were female. 50 male students said they were right-handed, and 10 female said they are left-handed.
How many male students were in the study?
State the proportion of students that are left-handed.
State the proportion of male students that are left-handed.
A small magazine asked people from different states to send in a vote on whether they supported Daylight Saving Time. The diagram shows the proportion of people that voted YES or NO in NSW, ACT and QLD:
State the proportion of people who voted "YES".
State the proportion of "NO" votes that are from NSW.
Considering just the voters from NSW and ACT, state the proportion of the votes that are NSW "YES" votes.
The Venn diagram shows the decisions of 535 consumers choosing to buy an iPhone and consumers choosing to buy a Blackberry:
If a consumer is selected at random, find the probability that he chose to buy:
A Blackberry.
A Blackberry only.
Both phones.
An iPhone or a Blackberry.
Neither phones.
An iPhone but not a Blackberry.
The Venn diagram depicts the investment choices of 1232 investors:
Find the probability that an investor randomly selected has investments in:
Bonds
Bonds and real estate.
Bonds or real estate.
Bonds and real estate but not shares.
Shares, bonds and real estate.
Real estate and shares but not bonds.
Shares, bonds or real estate.
A florist collected a sample of her flowers and divided them into the appropriate categories. as shown in the Venn diagram:
Find the probability that a flower is:
Not red but has thorns.
Not red and does not have thorns.
In a group of 183 primary and senior students, 96 are primary students. The students fell into three categories of travel to school - by bus, car, or walking. 113 students get to school by bus, 60 are primary students. 48 students get to school by car, 25 are primary students.
How many senior students catch the bus to school?
How many senior students are there in total?
Find the probability that a senior student walked to school.
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.
What proportion of responders are vegetarian?
What proportion of adults are vegetarian?
99 students were asked if they choose to study on the night before an exam or choose to party. 51 students choose to party while 59 choose to study. 10 neither choose to study nor party.
Find the number of students that chose to study and party
Find the probability that a student chosen at random chose:
Not to party.
To study and party.
To study only.
To study or party.
The employees of Pentagonal Plumbing 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
72 would go to a theme park
16 would only go to either a restaurant or a bowling alley
27 would only go to either a bowling alley or the theme park
17 would only go to either a restaurant or the theme park
8 would not go to a restaurant or a bowling alley or to the theme park
6 would go to all three places.
How many people in total work at Pentagonal Plumbing?
Given that the restaurant isn't available, state the proportion of the employees who still have another option.
Out of 100 students in a school, there are 55 students who are taking Physics classes, 50 students who are taking Chemistry classes and 15 students who are not enrolled in Physics or Chemistry classes.
Find the probability that the student is:
Taking Physics classes only.
Taking Chemistry classes only.
Taking both Physics and Chemistry classes.