Constructing three event Venn diagrams | Maths | Quizalize & Oak National Academy

Starter quiz

This probability Venn diagram shows the probability of a random spinner (spun once) landing on a square number or a factor of 36. Which of these probability statements are correct?

$a + b + c = 1$

P(factor of 36) = $b+c$ ✓

P(square ∪ factor of 36) = $a+c$

P(factor of 36 ∪ square) = $1-d$ ✓

P(factor of 36 |square) = $c$
This probability Venn diagram shows the probability of a random spinner (spun once) landing on a square number or a factor of 36. The value of $x$ is ______. Give your answer as a decimal.

'0.06' ✓
Here is a frequency Venn diagram. P(A ∩ B) = 0.2. The value of $x$ is ______.

'3' ✓
P(C given D) = 0.4. Which of these equations is correct to find the value of $x$ ?

$\frac{2x}{4x+1}=0.4$ ✓

$\frac{2x}{2x+1}=0.4$

$\frac{2x+1}{4x+1}=0.4$

$\frac{2x+1}{2x}=0.4$
A pack of cards contains 50 “character” (c) cards and some “spell” (s) cards. A card is taken at random, replaced and a 2nd card is taken. P(two spell cards) = 0.25. There are ______ cards in the deck.

'100' ✓
The ratio of cats (c) to dogs (d) in an animal shelter is 4 : 3. Two random animals are taken from the shelter for adoption. Find an expression for P(2 dogs).

$\frac{3}{7}$

$\frac{9}{49}$

$\frac{(3x-1)}{(7x-1)}$

$\frac{3(3x-1)}{7(7x-1)}$ ✓

$\frac{3(3x-1)}{49x}$

Exit quiz

A __________ space is all the possible outcomes of a trial.

frequency

population

probability

sample ✓
Izzy asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. ______ pupils take music but not drama.

'6' ✓
Izzy asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. ______ pupils do not take drama.

'17' ✓
A spinner is numbered with the integers from 80 to 89. The incomplete outcome Venn diagram is used to display 3 events. Select the correct statements.

Event A is {multiples of 4}

{prime numbers} is a subset of {odd numbers} ✓

{prime numbers} and {odd numbers} are mutually exclusive

{prime numbers} and {multiples of 4} are mutually exclusive ✓

Event C has 3 elements. ✓
What region is shown shaded in this Venn diagram?

A'

B' ∪ C'

A ∪ B' ∪ C'

A ⋂ B′ ⋂ C′ ✓

A ∪ B′ ⋂ C′
What region is shown shaded in this Venn diagram?

B ⋂ C′

A ∪ (B ⋂ C)′

(B ⋂ C)′ ✓

A ∪ B′ ⋂ C′

A ∪ B′ ∪ C

Worksheet

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Lesson Details

Key learning points

A three event Venn diagram is easier to complete if information from intersecting events is completed first
Venn diagrams may show probabilities, frequencies or outcomes
A three event Venn diagram may have some (or all) events being mutually exclusive
A three event Venn diagram may have events which are subsets of other events

Common misconception

There is often a lot of information to process, in order to complete a three event Venn diagram accurately. Pupils may confuse which region to complete.

A three event Venn diagram is easier to complete if information from intersecting events is completed first.

Keywords

Outcome - An outcome is a result of a trial (e.g. getting heads when flipping a coin once or getting two heads when flipping a coin twice).
Sample space - A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.
Event - An event is a subset of a sample space. i.e. An outcome or set of outcomes that may occur from a trial (e.g. flipping a coin twice and getting the same result each time).
Mutually exclusive - Two or more events are mutually exclusive if they share no common outcome.
Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.