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 $P(A \cap B')$ .
Level 2 · 2 marksTry it
2
For events $A$ and $B$ , $P(A) = 0.5$ , $P(B) = 0.4$ and $P(A \cap B) = 0.2$ . Find $P(A \cup B)$ .
Level 2 · 2 marksTry it
3
Events $A$ and $B$ are independent, with $P(A) = 0.4$ and $P(B) = 0.5$ .
(a) Find $P(A \cap B)$ . (2 marks)
(b) Find $P(A \cup B)$ . (2 marks)
Level 2 · 4 marksTry it
4
For events $A$ and $B$ , $\; P(A) = 0.62$ and $P(A \cap B) = 0.25$ .

Find $P(A \cap B')$ . (2 marks)
Level 2 · 2 marksTry it
5
SECTION B: STATISTICS

Two events $A$ and $B$ are such that

$\mathrm{P}(A) = 0.4$ , $\quad \mathrm{P}(B) = 0.55$ , $\quad \mathrm{P}(A \cup B) = 0.73$ .
(a) Find $\mathrm{P}(A \cap B)$ . (2 marks)
(b) Determine whether the events $A$ and $B$ are independent. (2 marks)
(c) Find $\mathrm{P}(A' \cap B')$ . (2 marks)
Level 2 · 6 marksTry it