GCSE · Venn diagrams & set notation

Probability from Venn diagramsExam-style questions

Why the denominator is always the total in the universal set — outsiders included — where P(A ∪ B) = P(A) + P(B) − P(A ∩ B) comes from in the picture, and how a "given that" condition shrinks the denominator to one circle.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$120$ people were asked whether they own a bicycle ( $A$ ) and whether they have a gym membership ( $B$ ). The Venn diagram shows the results.One of the $120$ people is chosen at random.

(a) Find $P(A \cap B)$ .

(b) Determine whether the events $A$ and $B$ are independent. You must show your working.

(c) Ben says that $A$ and $B$ are mutually exclusive. Is Ben correct? Give a reason for your answer.
Level 5 · 6 marksTry it
2
The Venn diagram shows the probabilities for two events $A$ and $B$ . The probability that neither $A$ nor $B$ occurs is $x$ .(a) Find the value of $x$ .

(b) Find $P(A')$ .

(c) Given that $B$ occurs, find the probability that $A$ also occurs.
Level 5 · 6 marksTry it