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4 marksCounting

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

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.

Determine the probability that at least one pencil taken from the bag is blue.

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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)(i)Draw a tree diagram to represent the possible events and their respective probabilities.[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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