Probabilities in three event Venn diagrams | Maths | Quizalize & Oak National Academy

Starter quiz

An ______ is a result of a trial in a probability experiment.

'outcome' ✓
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 drama but not music.

'5' ✓
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 music.

'16' ✓
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 B is {multiples of 4}.

{odd numbers} and {multiples of 4} are mutually exclusive. ✓

Event B has 3 elements.

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

{prime numbers} is a subset of {odd numbers}. ✓
What region is shown shaded in this Venn diagram?

A ∪ B' ∪ C

A ∩ C ∪ B'

B' ✓

A ∪ C

B' ∩ (A ∪ C)
What region is shown shaded in this Venn diagram?

(A ⋂ B) ⋂ (A ⋂ C) ⋂ (B ⋂ C)

(A ⋂ B) ⋃ (A ⋂ C) ⋃ (B ⋂ C) ✓

(A ⋃ B) ⋂ (A ⋃ C) ⋂ (B ⋃ C)

A' ⋃ B' ⋃ C'

A' ⋂ B' ⋂ C'

Venn diagrams are a representation used to model statistical and probability questions. Commonly circles are used to represent...

events ✓

frequencies

outcomes

probabilities
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 ∩ D).

$2 \over30$

$3 \over30$

$5 \over30$

$7 \over30$ ✓

$13 \over30$
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 ⋃ D′).

$15 \over30$

$18 \over30$

$19 \over30$

$20 \over30$

$21 \over30$ ✓
Here is a frequency Venn diagram. P(A ∩ B ∩ C) = ______. Give your answer as a decimal.

'0.14' ✓
Here is a frequency Venn diagram. P(A′ ⋃ B' ⋃ C) = ______. Give your answer as a decimal.

'0.88' ✓
$This frequency Venn diagram has 80 outcomes altogether. P(A ∩ B ∩ C) = <Math>\frac{1}{20}</Math>, P(A | B) = <Math>\frac{1}{3}</Math> and P(A ⋃ B) = 0.7. <Math>x</Math> = <span class="blank">______</span>.$

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. $x$ = ______.

'8' ✓

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A three event Venn diagram can be used to calculate probabilities
Three event Venn diagrams can be used to calculate the probability of a subset of events occurring
A three event Venn diagram can be used to calculate conditional probabilities
Three event Venn diagrams can be used to calculate conditional probabilities involving sets of events

Pupils may give the probability as a fraction with the wrong denominator.

Check that pupils understand the difference between the probability of event A given B, P(A|B), and the probability of event A and B occurring.

Venn diagrams - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.
Mutually exclusive - Mutually exclusive events have no outcomes in common.
Conditional probability - Conditional probability is the probability of an outcome occurring given that another event has occurred.