Venn diagrams  » More

Maths year 10/11: Venn diagrams, Sets {}, Unions ∪ , Intersections , Universal U

Sets { }

A set is a collection of things.
e.g. 2, 3, 5, 7, 11 is a set of prime numbers
and 2, 4, 6, 8, 10 is a set of even numbers

We write Sets inside curly brackets: Prime = {2, 3, 5, 7, 11}

We can also draw a picture like this:

Q: Write the set Even made from 2, 4, 6, 8, 10

ANS

If you show the numbers as Prime OR even numbers it is called a Union of sets with the symbol ∪

Prime ∪ Even = {2, 3, 4, 5, 6, 7, 8, 10, 11}

Not all numbers are in this set - some odd numbers are missing.
The results can be shown in a Venn diagram

Q1: What information can you obtain from the Venn diagram

Q2: For the numbers 1 to 16 show Even ∪ Square numbers

ANS

If you show the numbers as Even AND Prime it is called an Intersection of sets with the symbol

Prime Even = {2}

The results can be shown in a Venn diagram

Q: For the numbers 1 to 16 show Even Square numbers

ANS

Look at the Venn diagram for two sets.

Shade the region that represents P(A' B')

A' means NOT A

ANS

Look at the Venn diagram for 3 sets

Shade the region that represents P(M O')

O' means NOT O

ANS

80 children were asked if they preferred Milk or Orange juice.

70 prefer at least one of the drinks

35 prefer milk, but not orange juice

24 prefer orange juice, but not milk

Q1: Complete the Venn diagram, writing the number of children in each part.

Q2: One of the children is picked at random. Work out P(M O).

ANS

A class of 43 pupils were asked if they owned a phone or a tablet.

11 said they owned both

18 said they owned a tablet

34 said they owned a phone

Draw a Venn diagram to show the information.

ANS

A group of pupils were asked about their liking for English and Maths.

The information is shown on the Venn diagram.

Q1: How many pupils were asked

Q2: A pupil wa selected at random
What is the probability that they like both Maths and English

Q3: Given that a pupil does not like Maths
Find the probability that they don't like English.

ANS

A set of pupils were asked which TV programs they watched.

They were given the following options: CBBC, Paw Patrol, Dr Who or None.

Here is a list of TV programs they watched:

 Program Name CBBC Henry, Sue, Jess, Pops, Lou, Dave Paw Patrol Stu, Jess, Dave, Jane Dr Who Kath, Dave, Jane, Matt, Lou None Bill

Draw a Venn diagram to show the information.

ANS

David asked 100 people which drink they liked from Coffee, Tea or Milk.

9 people liked all three drinks
21 people liked milk and coffee
25 people liked milk and tea
24 people liked tea and coffee
53 people liked tea
53 people liked coffee
51 people liked milk

How many people did not like tea, coffee or milk.

ANS

Given that the person selected at random from 100 people liked tea find the probability that they also liked coffee.

ANS

There are 250 pupils in Year 11 taking some, if not all, of these exams: French, History and Drama.

92 pupils are taking History and Drama but not French
96 pupils are taking French and Drama but not History
95 pupils are taking History and French but not Drama
80 pupils are taking all three exams
127 are taking Drama in total
132 are taking French in total
126 are taking History in total

How many pupils do not take any of these exams?

ANS

Given that a pupil selected at random took one of these exams find the probability that they only took Drama.

ANS

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