Conditional probability in a Venn diagram

Download all resources

Previous lesson

Next lesson

Skip to lesson content

Share lesson with pupils

Lesson slides

Download lesson slides (PPTX)

Skip lesson slides (PPTX)

Lesson details

Learning outcome

I can calculate a conditional probability from a Venn diagram.

Key learning points

A Venn diagram can be used to calculate conditional probabilities
A Venn diagram can be used to calculate conditional probabilities involving sets of events
Venn diagrams allow us to identify which events are mutually exclusive
Venn diagrams can be used to identify which events are independent

Keywords

Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.
Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Conditional probability - Conditional probability is the probability of an outcome occurring given that another event has occurred.
Independent events - Event A is independent of event B if the probability of event A occurring is not affected by whether or not event B occurs.
Mutually exclusive - Mutually exclusive events have no outcomes in common.

Common misconception

Pupils may confuse the probability of event A given B, P(A|B), with the probability of event A and B occurring.

Use the context of the question to make a judgement about what probability is to be calculated. Try to avoid using, or draw attention to, potentially ambiguous language/notation. E.g. Is P(AB) referring to P(A given B) or P(B given A) or P(A and B)?

Teacher tip

Encourage pupils to draw/copy the Venn diagram and highlight or shade the regions that are needed for a given question.

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0

except where otherwise stated. See Oak's terms & conditions

(Collection 2).

Lesson video

Skip lesson video

Worksheet

Download worksheet (PPTX/PDF)

Skip worksheet (PPTX/PDF)

Prior knowledge starter quiz

Download starter quiz questions (PDF)

6 Questions

Q1.
Event A is of event B if the probability of event A occurring is not affected by whether or not event B occurs.

Correct Answer: independent

Q2.
Select the example of events which are not independent.

Rolling a die and then flipping a coin

Flipping three coins together

Rolling two dice together

Taking a counter at random from a box, replacing it and then taking another

Correct answer: Taking a counter at random from a box, keeping it and then taking another

Q3.
The table shows the types of marble in a bag. Match each event to its probability.

Correct Answer:P(blue),$$27\over 60$$

$$27\over 60$$

Correct Answer:P(green),$$33\over 60$$

$$33\over 60$$

Correct Answer:P(blue and has no swirl), $$12\over 60$$

$$12\over 60$$

Correct Answer:P(blue given it has no swirl),$$12\over 27$$

$$12\over 27$$

Correct Answer:P(green and has a swirl),$$18\over60$$

$$18\over60$$

Correct Answer:P(green given it has swirl),$$18\over 33$$

$$18\over 33$$

Q4.
A marble is taken at random from a box of marbles. Alex works out that P(swirl given it is blue) = P(swirl). This shows the event 'has a swirl' is __________ of the event 'blue marble'.

conditional

exhaustive

Correct answer: independent

mutually exclusive

Q5.
A 10-sided die with integers from 1 to 10 written on it is rolled once. Select the pair of mutually exclusive events.

Correct answer: A factor of 9

A factor of 10

Correct answer: Even number

Odd number

Prime number

Q6.
A deck of cards has a number on it (either prime or non-prime), and a symbol (a circle, square, or wave). A card is selected at random from the deck. Find P(non-prime | wave).

Correct answer: $$7\over18$$

$$7\over25$$

$$7\over56$$

$$25\over56$$

$$18\over56$$

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
Event A and event B are mutually exclusive events. Which of these statements are correct?

Correct answer: P(A and B) = 0

P(A or B) = 0

Correct answer: P(B | A) = 0

Correct answer: P(A | B) = 0

P(A) + P(B) = 0

Q2.
From the frequency Venn diagram, P(A | B) = . Give your answer as a decimal.

Correct Answer: 0.7

Q3.
From the frequency Venn diagram, P(A | B') = . Give your answer as a decimal.

Correct Answer: 0.7

Q4.
The diagram shows the number of outcomes for two events A and B. The values of P(A | B) and P(A | B') show that events A and B are events.

Correct Answer: independent

Q5.
Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) = $$3 \over 10$$. The value of $$x$$ is .

Correct Answer: 10

Q6.
Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) = $$3 \over 10$$. The value of $$y$$ is .

Correct Answer: 70

To help you plan your 11 maths lesson on: Conditional probability in a Venn diagram, download all teaching resources for free and adapt to suit your pupils' needs...

Conditional probability in a two-way table

Previous lesson

Conditional probability in a tree diagram

Next lesson

Choose exam board for KS4 Biology

Choose exam board for KS4 Chemistry

Choose exam board for KS4 Combined science

Choose exam board for KS4 Computer Science (GCSE)

Choose exam board for KS4 English

Choose exam board for KS4 French

Choose exam board for KS4 Geography

Choose exam board for KS4 German

Choose exam board for KS4 History

Choose tier for KS4 Maths

Choose exam board for KS4 Music

Choose exam board for KS4 Physical education (GCSE)

Choose exam board for KS4 Physics

Choose exam board for KS4 Religious education (GCSE)

Choose exam board for KS4 Spanish

Conditional probability in a Venn diagram

Lesson slides

Lesson details

Learning outcome

Key learning points

Keywords

Common misconception

Teacher tip

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Event A is of event B if the probability of event A occurring is not affected by whether or not event B occurs.

Q2.Select the example of events which are not independent.

Q3.The table shows the types of marble in a bag. Match each event to its probability.

Q4.A marble is taken at random from a box of marbles. Alex works out that P(swirl given it is blue) = P(swirl). This shows the event 'has a swirl' is __________ of the event 'blue marble'.

Q5.A 10-sided die with integers from 1 to 10 written on it is rolled once. Select the pair of mutually exclusive events.

Q6.A deck of cards has a number on it (either prime or non-prime), and a symbol (a circle, square, or wave). A card is selected at random from the deck. Find P(non-prime | wave).

Assessment exit quiz

6 Questions

Q1.Event A and event B are mutually exclusive events. Which of these statements are correct?

Q2.From the frequency Venn diagram, P(A | B) = . Give your answer as a decimal.

Q3.From the frequency Venn diagram, P(A | B') = . Give your answer as a decimal.

Q4.The diagram shows the number of outcomes for two events A and B. The values of P(A | B) and P(A | B') show that events A and B are events.

Q5.Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) = $$3 \over 10$$. The value of $$x$$ is .

Q6.Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) = $$3 \over 10$$. The value of $$y$$ is .

How to plan a lesson using our resources

Q1.
Event A is of event B if the probability of event A occurring is not affected by whether or not event B occurs.

Q2.
Select the example of events which are not independent.

Q3.
The table shows the types of marble in a bag. Match each event to its probability.

Q4.
A marble is taken at random from a box of marbles. Alex works out that P(swirl given it is blue) = P(swirl). This shows the event 'has a swirl' is __________ of the event 'blue marble'.

Q5.
A 10-sided die with integers from 1 to 10 written on it is rolled once. Select the pair of mutually exclusive events.

Q6.
A deck of cards has a number on it (either prime or non-prime), and a symbol (a circle, square, or wave). A card is selected at random from the deck. Find P(non-prime | wave).

Q1.
Event A and event B are mutually exclusive events. Which of these statements are correct?

Q2.
From the frequency Venn diagram, P(A | B) = . Give your answer as a decimal.

Q3.
From the frequency Venn diagram, P(A | B') = . Give your answer as a decimal.

Q4.
The diagram shows the number of outcomes for two events A and B. The values of P(A | B) and P(A | B') show that events A and B are events.

Q5.
Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) = $$3 \over 10$$. The value of $$x$$ is .

Q6.
Here is an incomplete frequency Venn diagram. P(C) = $$1\over3$$, P(D') = $$1\over6$$, P(C ∩ D) = $$1 \over 4$$ and P(C | D) = $$3 \over 10$$. The value of $$y$$ is .