New
New
Year 9

Using a Venn diagram to display outcomes for more than two events

I can systematically find all the possible outcomes for more than two events by using a Venn diagram.

New
New
Year 9

Using a Venn diagram to display outcomes for more than two events

I can systematically find all the possible outcomes for more than two events by using a Venn diagram.

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Lesson details

Key learning points

  1. Possible outcomes for more than two events can be shown in a Venn diagram.
  2. The Venn diagram can be used to generate either an outcome tree or a list.
  3. A Venn diagram can be generated from either an outcome tree or a list.

Keywords

  • Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

Common misconception

Pupils may struggle with the phrasing and language, when trying to identify the correct regions of the Venn diagram.

Encourage the pupils to describe each region of the Venn diagram, in context where appropriate.

You may wish to create a physical Venn diagram for three events and place the pupils in the relevant regions of the Venn diagram. This helps to build the language and familiarity with the Venn diagram.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Venn diagrams are a representation used to model statistical/probability questions. Usually are used to represent events.
Correct Answer: circles, circle
Q2.
A Venn diagram has a sample space of {integers from 1 to 16 inclusive}, event A = {square numbers} and event B = {odd numbers}. Select the outcomes that are in both event A and event B.
Correct answer: 1
4
Correct answer: 9
16
25
Q3.
Which of these symbols represents the sample space on a Venn diagram?
$$\pi$$
Correct answer: $$\xi$$
$$\emptyset$$
$$\Omega$$
Q4.
This Venn diagram shows some sandwich orders. The choices are white (W) or brown (B) bread and the filling can be cheese (C) or ham (H). Which pupil had a cheese sandwich made with brown bread?
An image in a quiz
Alex
Andeep
Jun
Lucas
Correct answer: Sam
Q5.
This Venn diagram shows some sandwich orders. You can have white (W) or brown (B) bread and the filling can be cheese (C) or ham (H). Which pupils had a ham sandwich?
An image in a quiz
Alex
Correct answer: Andeep
Jun
Correct answer: Lucas
Sam
Q6.
Which outcome tree matches this Venn diagram?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz

6 Questions

Q1.
Which of the Venn diagrams is always correct for three events?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q2.
Which description best describes the region that is shaded on this Venn diagram?
An image in a quiz
Outcomes that are in event A and event B but not in event C.
Outcomes that are in event A and event C but not in event B.
Correct answer: Outcomes that are in event B and event C but not in event A.
Q3.
Which description best describes the region that is shaded on this Venn diagram?
An image in a quiz
Outcomes that are in event A, event B and event C.
Outcomes that are in event A, event B or event C.
Outcomes that are not in event A and event B and event C.
Correct answer: Outcomes that are not in event A nor event B nor event C.
Q4.
This outcome tree shows a sample space, organised into three events. Where would {3, 5} be on a Venn diagram showing the same sample space?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q5.
Which of the outcomes from the sample space shown on the outcome tree would be in the shaded region of a Venn diagram showing the same information?
An image in a quiz
{7, 11}
{9}
{2}
Correct answer: {6, 10}
{4, 8, 12}
Q6.
Match each numbered region on the Venn diagram to the correct outcomes.
An image in a quiz
Correct Answer:region 1,{9}

{9}

Correct Answer:region 2,{1}

{1}

Correct Answer:region 3,{7, 11}

{7, 11}

Correct Answer:region 4,{2}

{2}

Correct Answer:region 5,$$\emptyset$$

$$\emptyset$$

Correct Answer:region 6,{4, 8, 12}

{4, 8, 12}