A-level · Probability

Venn diagramsExam-style questions

Using a Venn diagram to organise events: the intersection A∩B ("and"), the union A∪B ("or"), and the complement A′ ("not"); filling in the regions from the numbers in a problem (starting with the overlap); reading probabilities off the diagram; and the addition formula P(A∪B) = P(A) + P(B) − P(A∩B).

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18 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The Venn diagram shows probabilities for events $A$ and $B$ . Find $P(A \cup B)$ .
Level 2 · 2 marksTry it
2
A museum surveyed $90$ $90$ of its visitors about the facilities they used during their visit. The three facilities were:
- the café ( $C$ )
- the gift shop ( $G$ )
- the audio guide ( $A$ )
The table below shows how many of the $90$ $90$ visitors used each facility or combination of facilities.
Used Number of visitors
$C$ $46$
$G$ $32$
$A$ $22$
$C$ and $G$ $15$
$C$ and $A$ $10$
$G$ and $A$ $7$
$C$ , $G$ and $A$ $4$
(a) Represent this information by fully completing the Venn diagram below.(3 marks)
(b) A visitor in the survey is picked at random.

Find the probability that this visitor used the gift shop only.

(1 mark)
Level 2 · 4 marksTry it
3
For events $A$ and $B$ , $P(A) = 0.5$ , $P(B) = 0.3$ and $P(A \cap B) = 0.1$ .
(a) Find $P(A \cap B')$ .
(b) Find $P(A' \cap B')$ .
Level 3 · 4 marksTry it
4
In a group of $50$ students, $30$ study Maths, $25$ study Physics and $15$ study both. A student is chosen at random. Find the probability they study Maths but not Physics.
Level 3 · 2 marksTry it
5
For events $A$ and $B$ , $P(A) = 0.45$ , $P(B) = 0.35$ and $P(A \cup B) = 0.6$ . Find $P(A \cap B)$ .
Level 3 · 2 marksTry it

Used	Number of visitors
$C$	$46$
$G$	$32$
$A$	$22$
$C$ and $G$	$15$
$C$ and $A$	$10$
$G$ and $A$	$7$
$C$ , $G$ and $A$	$4$

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