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Lesson 16 of 18

Year 11
Higher

Comparing multiple representations to calculate conditional probabilities

I can compare and contrast the usefulness of the different representations when calculating conditional probabilities.

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Lesson 16 of 18

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Year 11
Higher

Comparing multiple representations to calculate conditional probabilities

I can compare and contrast the usefulness of the different representations when calculating conditional probabilities.

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Lesson details

Key learning points

The same conditional probability can be found from multiple representations
Each representation can be compared to see how conditional probabilities are calculated
Information from one representation can be displayed in a different representation
The preferred representation may change depending on the context

Keywords

Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Probability tree - Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.
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.
Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

Common misconception

Pupils may think that only one type of diagram/table can be used to represent each probability problem and worry about choosing the correct one.

Emphasise that the same probability problem can often be represented using multiple diagrams or tables. In many cases, they will be able to find what they are looking for in any representation but it may be clearer to see in some more than others.

To help you plan your year 11 maths lesson on: Comparing multiple representations to calculate conditional probabilities, download all teaching resources for free and adapt to suit your pupils' needs...

Ask pupils to find the same probability using multiple diagrams. Then ask them to discuss which diagram was most useful for finding that particular probability and why.

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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).

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Prior knowledge starter quiz

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6 Questions

Q1.
The probability of an outcome occurring given that another event has occurred is called probability.

Correct Answer: conditional

Q2.
Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ⋃ M).

$$ 22 \over 30$$

$$ 26 \over 30$$

$$ 27 \over 30$$

Correct answer: $$ 25 \over 30$$

$$ 28 \over 30$$

Q3.
Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ∩ M ∩ D').

Correct answer: $$1 \over30 $$

$$2 \over30 $$

$$3 \over30 $$

$$5 \over30 $$

$$8 \over30 $$

Q4.
Here is a frequency Venn diagram. P(A ⋃ B ⋃ C) = . Give your answer as a decimal.

Correct Answer: 0.93

Q5.
Here is a frequency Venn diagram. P(A ⋃ C′) = . Give your answer as a decimal.

Correct Answer: 0.76

Q6.
This frequency Venn diagram has 80 outcomes altogether. P(A ∩ B ∩ C) = $$\frac{1}{20}$$, P(A | B) = $$\frac{1}{3}$$ and P(A ⋃ B) = 0.7. $$y$$ = .

Correct Answer: 6

Assessment exit quiz

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6 Questions

Q1.
Two spinners are spun once each. The table shows the outcomes for each spinner. Match each value from the frequency tree to its value.

Correct Answer:$$a$$,24

Correct Answer:$$b$$,9

Correct Answer:$$d$$,6

Correct Answer:$$f$$,10

Q2.
An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$a$$ = .

Correct Answer: 270

Q3.
An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$d$$ = .

Correct Answer: 200

Q4.
An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$x$$ is .

Correct Answer: 14

Q5.
An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$w$$ is .

Correct Answer: 11

Q6.
A game developer tested to see whether a playable character was more likely to win (W) with a rebalance (R) of the character’s stats or not. P(RW') = . Give your answer as a decimal.

Correct Answer: 0.32

Comparing multiple representations to calculate conditional probabilities

Comparing multiple representations to calculate conditional probabilities

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.The probability of an outcome occurring given that another event has occurred is called probability.

Q2.Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ⋃ M).

Q3.Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ∩ M ∩ D').

Q4.Here is a frequency Venn diagram. P(A ⋃ B ⋃ C) = . Give your answer as a decimal.

Q5.Here is a frequency Venn diagram. P(A ⋃ C′) = . Give your answer as a decimal.

Q6.This frequency Venn diagram has 80 outcomes altogether. P(A ∩ B ∩ C) = $$\frac{1}{20}$$, P(A | B) = $$\frac{1}{3}$$ and P(A ⋃ B) = 0.7. $$y$$ = .

Assessment exit quiz

6 Questions

Q1.Two spinners are spun once each. The table shows the outcomes for each spinner. Match each value from the frequency tree to its value.

Q2.An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$a$$ = .

Q3.An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$d$$ = .

Q4.An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$x$$ is .

Q5.An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$w$$ is .

Q6.A game developer tested to see whether a playable character was more likely to win (W) with a rebalance (R) of the character’s stats or not. P(RW') = . Give your answer as a decimal.

Q1.
The probability of an outcome occurring given that another event has occurred is called probability.

Q2.
Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ⋃ M).

Q3.
Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ∩ M ∩ D').

Q4.
Here is a frequency Venn diagram. P(A ⋃ B ⋃ C) = . Give your answer as a decimal.

Q5.
Here is a frequency Venn diagram. P(A ⋃ C′) = . Give your answer as a decimal.

Q6.
This frequency Venn diagram has 80 outcomes altogether. P(A ∩ B ∩ C) = $$\frac{1}{20}$$, P(A | B) = $$\frac{1}{3}$$ and P(A ⋃ B) = 0.7. $$y$$ = .

Q1.
Two spinners are spun once each. The table shows the outcomes for each spinner. Match each value from the frequency tree to its value.

Q2.
An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$a$$ = .

Q3.
An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$d$$ = .

Q4.
An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$x$$ is .

Q5.
An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$w$$ is .

Q6.
A game developer tested to see whether a playable character was more likely to win (W) with a rebalance (R) of the character’s stats or not. P(RW') = . Give your answer as a decimal.