Lesson Element – 11.02c Venn Diagrams

Task 1 – Shading Venn diagrams
A group of athletes were asked whether or
not they were members of the local sports
centre. They were also asked if they had
entered a competition this month.
Working in pairs or as individuals match
up each Venn diagram with the correct
statement.
Member
of sports
centre
Members of the sports centre who have
entered a competition this month.
Entered a
competition
May 2015

Member
of sports
centre
Athletes who have entered a competition
this month.
Entered a
competition
Member
of sports
centre
Athletes who are not members of the
sports centre.
Entered a
competition
May 2015

Member
of sports
centre
Athletes who have not entered a
competition this month.
Entered a
competition
Member
of sports
centre
All of the athletes.
Entered a
competition
May 2015

Member
of sports
centre
Members of the sports centre.
Entered a
competition
Member
of sports
centre
Entered a
competition
May 2015
Athletes who have entered a competition
this month, but are not members of the
sports centre.

Member
of sports
centre
Athletes who are members of the sports
centre or have entered a competition this
month.
Entered a
competition
Member
of sports
centre
Entered a
competition
May 2015
Athletes who are not members of the
sports centre and have not entered a
competition this month.
Task 2 – Membership of sets
Each Venn diagram should have 4 dots in A, 4 dots in B and 4 dots in C.
Using the blank Venn diagrams, investigate how many different ways there are of placing the dots to
meet the requirement?
A
B
A
C
A
C
B
A
C
A
A
C
July 2015
B
C
B
C
B
C
B
A
B
A
B
C
Task 3 – Venn diagram puzzle
Use the clues on the cards to complete the Venn diagram.
Swimming
Pool
Fitness
Centre
Squash Court

A sports centre took a survey of
its customers leaving the centre
one day. The customers were
asked which, if any, of the three
facilities they had just used.
July 2015
The probability that a customer
1 .
used all three facilities was
70
The probability that a customer
who used the fitness centre also
3 .
used the squash court was
20

The probability that a customer
who used the fitness centre also
used the swimming pool was 1 .
5
7 people used the squash court.
The probability that a customer
used the swimming pool and the
squash court was the same as
the probability that a customer
used the squash court and the
fitness centre.
July 2015
44 people used just the swimming
pool.
The probability that a customer
used the swimming pool was 5 .
7
The probability that a customer
who used the squash court also
used the fitness centre was 3 .
7
Two customers didn’t use any of
the three facilities.
The probability that a customer
who used the squash court also
used the swimming pool was 3 .
7
2 people used just the squash
court.

50 people used the swimming
pool.
14 people used just the fitness
centre.
The probability that a customer
who used the swimming pool also
3 .
used the squash court was
50
The probability that a customer
used none of the three facilities
1 .
was
35
The probability that a customer
1 .
used the squash court was
10
July 2015
3 people used the squash court
and the swimming pool.
One customer used all three
facilities.
20 people used the fitness centre.
The probability that a customer
who used the swimming pool also
2 .
used the fitness centre was
25