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4 marksCounting

CAPE Pure Mathematics Unit 2 · May/June 2023 · Paper 2 · Question 5(b)(i)

A bag contains five yellow pencils, three blue pencils and four red pencils. Two pencils are taken out of the bag, at random, and are not replaced.

Draw a tree diagram to represent the possible events and their respective probabilities.

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Other parts of this question

  1. 5(a)(i)Calculate the determinant of M.[5 marks]
  2. 5(a)(ii)Hence, or otherwise, determine the values of k for which the simultaneous equations x + y - z = 1, x + 2y - kz = 0, x - ky - z = 1 have a unique solution.[4 marks]
  3. 5(a)(iii)Using k = 2 in the matrix, M, solve the system of linear equations by first reducing it to row echelon form.[6 marks]
  4. 5(b)(ii)Determine the probability that at least one pencil taken from the bag is blue.[4 marks]
  5. 5(b)(iii)Determine whether the result of the second draw is independent of the first draw. Justify your response.[2 marks]

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