Sets & Venn diagrams

A group of 100 pupils attended their school sports day.

13 pupils did not compete in either Track or Field events. The expressions in the following Venn diagram represent the number of pupils in each category. The universal set, ε, contains all the pupils.

Find the value of x.

One pupil is chosen at random from the group.

What is the probability that this pupil competed only in Track events?

A group of 100 pupils attended their school sports day.

13 pupils did not compete in either Track or Field events. The expressions in the following Venn diagram represent the number of pupils in each category. The universal set, ε, contains all the pupils.

Find the value of x.

One pupil is chosen at random from the group.

What is the probability that this pupil competed only in Track events?

At lunchtime on Wednesday, a café had 19 customers.

• 7 of these customers bought a meal and a drink. • 2 of these customers did not buy a meal or a drink. • The total number of customers who bought a meal was twice the total number of customers who bought a drink.

One of these customers is chosen at random.

What is the probability that this customer bought a meal?

At lunchtime on Wednesday, a café had 19 customers.

• 7 of these customers bought a meal and a drink. • 2 of these customers did not buy a meal or a drink. • The total number of customers who bought a meal was twice the total number of customers who bought a drink.

One of these customers is chosen at random.

What is the probability that this customer bought a meal?

A bus going to a Welsh Heritage conference has 43 people on board.

There are 38 students, 4 tutors and a driver on the bus.

At the conference, each student will attend a session on Language, a session on History or both sessions.

• All the students will attend at least one session. • 18 students will attend both sessions. • 25 students will attend the session on History. • The tutors and driver will not attend either of the sessions.

One of the people on the bus is chosen at random.

What is the probability that this person will attend the session on Language?

In a group of 200 people:

• 105 people do not have black hair and do not wear glasses • 20 people have black hair and wear glasses • 70 people have black hair.

In a group of 200 people:

• 105 people do not have black hair and do not wear glasses • 20 people have black hair and wear glasses • 70 people have black hair.

On each Venn diagram, shade the region that represents the given set.

On each Venn diagram, shade the region that represents the given set.

A group of pupils is asked whether they can speak Welsh, French, both languages, or neither language.

Their answers are shown in the Venn diagram below. The universal set, , contains all the pupils in the group.

How many of the pupils cannot speak French?

One pupil from the group is chosen at random.

What is the probability that this pupil can speak both Welsh and French?

A group of pupils is asked whether they can speak Welsh, French, both languages, or neither language.

Their answers are shown in the Venn diagram below. The universal set, , contains all the pupils in the group.

How many of the pupils cannot speak French?

One pupil from the group is chosen at random.

What is the probability that this pupil can speak both Welsh and French?

A Venn diagram is used to show the following information:

• The Universal set, ε, is the set of numbers from 10 to 20 inclusive. • Set A = {11, 13, 14, 18, 20}. • Set B = {multiples of 3}.

Draw the Venn diagram that shows the above information.

A Venn diagram is used to show the following information:

• The Universal set, ε, is the set of numbers from 10 to 20 inclusive. • Set A = {11, 13, 14, 18, 20}. • Set B = {multiples of 3}.

Draw the Venn diagram that shows the above information.

Place the numbers 1, 2, 3, 4, 5 in the Venn diagram below.

Space for working:

Display the following information in a Venn diagram.

• Universal Set (ε): Integers between 74 and 80 inclusive.

• Set A: Even numbers.

• Set B: Multiples of 3.

Display the following information in a Venn diagram.

• Universal Set (ε): Integers between 74 and 80 inclusive.

• Set A: Even numbers.

• Set B: Multiples of 3.

The Venn diagram below is used for showing square numbers and even numbers.

Place the numbers 1, 2, 3, 4 and 5 in the Venn diagram.

30 rugby supporters travel to Cardiff on a coach. They decide to investigate how many of them can sing one, or both, of the songs ‘Hen Wlad fy Nhadau’ and ‘Bread of Heaven’.

• 12 say they can sing both songs. • 18 say they can sing ‘Bread of Heaven’. • 5 say they cannot sing either of the songs.

Complete the Venn diagram below to show this information.

The universal set, , contains all of the 30 supporters on the coach.

One of these supporters is chosen at random.

What is the probability that this person can sing ‘Hen Wlad fy Nhadau’?

30 rugby supporters travel to Cardiff on a coach. They decide to investigate how many of them can sing one, or both, of the songs ‘Hen Wlad fy Nhadau’ and ‘Bread of Heaven’.

• 12 say they can sing both songs. • 18 say they can sing ‘Bread of Heaven’. • 5 say they cannot sing either of the songs.

One of these supporters is chosen at random.

What is the probability that this person can sing ‘Hen Wlad fy Nhadau’?

A group of 20 people visited Anglesey for a weekend break.

• 10 of the group visited Beaumaris Castle. • 13 of the group visited South Stack Lighthouse. • 4 of the group did not visit either of these places.

Complete the Venn diagram below to show this information.

The universal set, , contains all of the 20 people in the group.

One person is chosen at random from the group.

What is the probability that this person visited only one of the two places?

A group of 20 people visited Anglesey for a weekend break.

• 10 of the group visited Beaumaris Castle. • 13 of the group visited South Stack Lighthouse. • 4 of the group did not visit either of these places.

Complete the Venn diagram below to show this information.

The universal set, , contains all of the 20 people in the group.

One person is chosen at random from the group.

What is the probability that this person visited only one of the two places?