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Question 19

At a sports centre, three events are recorded for a randomly selected member:

  • JJJ: the member uses the gym
  • SSS: the member uses the swimming pool
  • TTT: the member plays tennis

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

  • P(only J)=0.25P(\text{only }J)=0.25P(only J)=0.25
  • P(only S)=0.16P(\text{only }S)=0.16P(only S)=0.16
  • P(only T)=0.20P(\text{only }T)=0.20P(only T)=0.20
  • P(J∩S)=pP(J\cap S)=pP(J∩S)=p
  • P(J∩T)=qP(J\cap T)=qP(J∩T)=q
  • P(S∩T)=rP(S\cap T)=rP(S∩T)=r
  • P(none of J,S,T)=0.09P(\text{none of }J,S,T)=0.09P(none of J,S,T)=0.09

Events J J\,J and T T\,T are mutually exclusive. Events J J\,J and S S\,S 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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