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).

Start practising Read the lesson

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
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
2
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
3
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
4
For events $A$ and $B$ , $P(A') = 0.6$ , $P(B) = 0.5$ and $P(A \cap B) = 0.2$ . Find $P(A \cup B)$ .
Level 3 · 2 marksTry it
5
In a survey of $80$ households, $35$ own a dog, $28$ own a cat and $12$ own both. A household is chosen at random. Find the probability it owns a dog or a cat (or both).
Level 3 · 2 marksTry it

1 more question on venn diagrams

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free