A-level · Probability

Set notation for eventsExam-style questions

Writing events with set notation — intersection ∩, union ∪ and complement ′ — matching each to a region of a Venn diagram, and the probability rules that go with them (P(A′) = 1 − P(A), P(A ∩ B′) = P(A) − P(A ∩ B)).

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

DifficultyAll Level 1 Level 2 Level 3 Level 4

1
For events $A$ and $B$ , $P(A) = 0.5$ , $P(B) = 0.4$ and $P(A \cap B) = 0.2$ . Find $P\big((A \cup B)'\big)$ .
Level 3 · 2 marksTry it
2
The Venn diagram shows the probabilities for two events $A$ and $B$ .
(a) Find $P(A)$ .
(b) Find the probability that exactly one of $A$ and $B$ occurs.
Level 3 · 2 marksTry it
3
For events $A$ and $B$ , $P(A) = 0.6$ , $P(B) = 0.5$ and $P(A \cap B) = 0.3$ . Find $P(A' \cap B')$ .
Level 3 · 2 marksTry it
4
Given that $P(A \cup B) = 0.85$ , find $P(A' \cap B')$ .
Level 3 · 2 marksTry it
5
For events $A$ and $B$ , $P(A) = 0.45$ , $P(B) = 0.6$ and $P(A \cup B) = 0.8$ .
(a) Find $P(A \cap B)$ .
(b) Find $P(A \cap B')$ .
Level 3 · 3 marksTry it

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