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Question 13

A school records three events for a randomly selected student:

  • GGG: the student studies geography
  • HHH: the student studies history
  • LLL: the student studies Latin

The Venn diagram for these events has the following region probabilities:

  • P(only G)=0.35P(\text{only }G)=0.35P(only G)=0.35
  • P(only H)=0.10P(\text{only }H)=0.10P(only H)=0.10
  • P(only L)=0.18P(\text{only }L)=0.18P(only L)=0.18
  • P(G∩H)=pP(G\cap H)=pP(G∩H)=p
  • P(G∩L)=qP(G\cap L)=qP(G∩L)=q
  • P(H∩L)=rP(H\cap L)=rP(H∩L)=r
  • P(none of G,H,L)=0.12P(\text{none of }G,H,L)=0.12P(none of G,H,L)=0.12

Events G G\,G and L L\,L are mutually exclusive. Events G G\,G and H H\,H are independent.

Find the values of ppp, q q\,q and rrr.

[5]
Markscheme

Probability Questions

  1. AS Level
  2. /Maths
  3. /Probability

34 exam-style questions on Edexcel AS Level Maths Probability, covering 5.1 Calculating Probabilities, 5.2 Venn Diagrams, 5.3 Mutually Exclusive and Independent Events, and 5.4 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.

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