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CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2 · Question 5(a)(i)

The given Venn diagram shows a sample space, S, and the probabilities of two events, A and B, within the sample space S.

Given that P(A \cup B) = 0.7, calculate P(A \text{ only}).

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Other parts of this question

  1. 5(a)(ii)Hence, determine whether events A and B are independent. Justify your answer.[2 marks]
  2. 5(b)(i)Represent the outcomes of the draws and their corresponding probabilities on a tree diagram.[4 marks]
  3. 5(b)(ii)Determine the probability that the second ball drawn is white.[3 marks]
  4. 5(c)(i)Show that AB = 20I.[5 marks]
  5. 5(c)(ii)Hence, deduce the inverse, A^{-1}, of the matrix A.[2 marks]
  6. 5(c)(iii)Hence, or otherwise, solve the system of linear equations given by: \begin{aligned} x - y + z &= 1 \\ x - 2y + 4z &= 5 \\ x + 3y + 9z &= 25 \end{aligned}[6 marks]

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