Comparing multiple representations to calculate conditional probabilities | Maths

Starter quiz

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

'conditional' ✓
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).

$22 \over 30$

$26 \over 30$

$27 \over 30$

$25 \over 30$ ✓

$28 \over 30$
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').

$1 \over30$ ✓

$2 \over30$

$3 \over30$

$5 \over30$

$8 \over30$
Here is a frequency Venn diagram. P(A ⋃ B ⋃ C) = ______. Give your answer as a decimal.

'0.93' ✓
Here is a frequency Venn diagram. P(A ⋃ C′) = ______. Give your answer as a decimal.

'0.76' ✓
$This frequency Venn diagram has 80 outcomes altogether. P(A ∩ B ∩ C) = <Math>\frac{1}{20}</Math>, P(A | B) = <Math>\frac{1}{3}</Math> and P(A ⋃ B) = 0.7. <Math>y</Math> = <span class="blank">______</span>.$

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. $y$ = ______.

'6' ✓

Exit quiz

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

$a$

⇔

24 ✓

$b$

⇔

9 ✓

$d$

⇔

6 ✓

$f$

⇔

10 ✓
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. $a$ = ______.

'270' ✓
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. $d$ = ______.

'200' ✓
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 ______.

'14' ✓
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 ______.

'11' ✓
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.

'0.32' ✓

Worksheet

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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

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.

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.