A-level · Probability

Conditional probabilityExam-style questions

The probability of A given B, P(A|B) = P(A ∩ B) / P(B), as restricting the sample space to B — reading it off a Venn diagram, the multiplication formula P(A ∩ B) = P(B)P(A|B), and testing independence with P(A|B) = P(A).

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28 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 $P(A \mid B)$ .
Level 3 · 2 marksTry it
2
The probability that it rains on a given day is $P(R) = 0.3$ . If it rains, the probability a match is cancelled is $P(C \mid R) = 0.8$ . Find $P(R \cap C)$ .
Level 3 · 2 marksTry it
3
For events $A$ and $B$ , $P(A) = 0.4$ , $P(B) = 0.5$ and $P(A \cap B) = 0.2$ . Determine whether $A$ and $B$ are independent.
Level 3 · 2 marksTry it
4
For events $A$ and $B$ , $P(A) = 0.3$ , $P(B) = 0.5$ and $P(A \cap B) = 0.2$ . Determine whether $A$ and $B$ are independent.
Level 3 · 2 marksTry it
5
For events $A$ and $B$ , $\; P(A) = 0.55$ , $P(B) = 0.4$ and $P(A \cup B) = 0.75$ .
(a) Find $P(A \cap B)$ . (2 marks)
(b) Find $P(A \mid B)$ and $P(B \mid A)$ , giving exact answers. (2 marks)
Level 3 · 4 marksTry it

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