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2 marksProbability Theory

CAPE Applied Mathematics Unit 1 · 2013 · Paper 2 · Question 3(a)(iii)a)

A third event Q is independent of T, with P(T ∩ Q) = 0.2 and P(R ∪ Q) = 0.7.

Find P(Q).

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Other parts of this question

  1. 3(a)(i)a)Find P(R ∩ T).[3 marks]
  2. 3(a)(i)b)Find P(R ∪ T).[3 marks]
  3. 3(a)(ii)Draw a clearly labelled Venn diagram showing the sets (R ∩ T'), (R ∩ T), (R' ∩ T), (R ∪ T)' and their respective probabilities.[3 marks]
  4. 3(a)(iii)b)Show that R and Q are mutually exclusive.[2 marks]
  5. 3(b)(i)How many people were in the survey?[2 marks]
  6. 3(b)(ii)a)Determine the probability that a randomly selected patron thought that there was an improvement in service.[3 marks]
  7. 3(b)(ii)b)Determine the probability that the patron was a female and she thought that there was no improvement in the service.[3 marks]
  8. 3(b)(ii)c)Given that the patron thought there was an improvement, what is the probability that the patron was a male?[4 marks]

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