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
In a group of $50$ students, $30$ play football ( $F$ ), $18$ play tennis ( $T$ ) and $8$ play both. A student is chosen at random.
(a) Find $P(F' \cap T')$ .
(b) Find $P(F \cap T')$ .
Level 4 · 3 marksTry it
2
The events $A$ and $B$ are such that

$\mathrm{P}(A) = 0.45, \qquad \mathrm{P}(B) = 0.3, \qquad \mathrm{P}(A \cup B) = 0.6$
(a) Find $\mathrm{P}(A \cap B)$ . (2 marks)
(b) Determine whether $A$ and $B$ are independent. (2 marks)
(c) Find $\mathrm{P}\left(A \mid B'\right)$ , giving your answer to $3$ significant figures. (3 marks)
(d) Find $\mathrm{P}\left(A' \cap B'\right)$ . (2 marks)
Level 4 · 9 marksTry it