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4 marksProbability Theory

CAPE Applied Mathematics Unit 1 · 2017 · Paper 2 · Question 3(a)(ii)

Two events, M and N, are such that P(M) = 4/5, P(M ∪ N) = 7/8, and P(M ∩ N) = 1/4.

State, with reason, whether M and N are independent, and whether M and N are mutually exclusive.

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Other parts of this question

  1. 3(a)(i)Calculate P(N).[3 marks]
  2. 3(b)(i)In the space provided, draw a clearly labelled tree diagram to show this information.[4 marks]
  3. 3(b)(ii)Calculate the probability that an item, selected at random, is defective.[3 marks]
  4. 3(b)(iii)Given that an item selected at random is defective, calculate the probability that it is an item for export. Give your answer correct to three significant…[3 marks]
  5. 3(c)(i)Determine the value of p.[2 marks]
  6. 3(c)(ii)Calculate E(X) and Var(X).[6 marks]

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