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

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    3030 members of a music club were asked whether they play the guitar (GG) and whether they play the violin (VV). The Venn diagram shows the results.ξ7GV968One member is chosen at random.

    (a) Find the probability that this member plays the violin.

    (b) Given that the chosen member plays the violin, find the probability that they also play the guitar.
    Level 4 · 4 marksTry it
  2. 2
    6060 students were asked which of swimming (SS), tennis (TT) and running (RR) they take part in. The Venn diagram shows the results.ξ15STR11976543One of the 6060 students is chosen at random.

    (a) Find the probability that the student takes part in all three activities.

    (b) Find the probability that the student swims.

    (c) Find the probability that the student takes part in exactly one of the three activities.
    Level 4 · 5 marksTry it