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CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2 · Question 5(a)

SECTION C (Module 3) Answer BOTH questions.

Three letters from the word BRIDGE are selected one after the other without replacement. When a letter is selected, it is classified as either a vowel (V) or a consonant (C). Use a tree diagram to show the possible outcomes (vowel or consonant) of the THREE selections. Show all probabilities on the diagram.

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  1. 5(b)(i)The augmented matrix for a system of three linear equations with variables x, y and z respectively is…[5 marks]
  2. 5(b)(ii)The augmented matrix for another system is formed by replacing the THIRD row of A in (i) above with (1 \; -5 \; 5 \mid 3). Determine whether the solution…[5 marks]
  3. 5(c)(i)A country, X, has three airports (A, B, C). The percentage of travellers that use each of the airports is 45\%, 30\% and 25\% respectively. Given…[5 marks]
  4. 5(c)(ii)On a particular day, a traveller was caught carrying a weapon at an airport in Country X. What is the probability that the traveller used airport C?[3 marks]

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