A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2019 · Q25 Marks

Benju cycles to work each morning and he has two possible routes. He chooses the hilly route with probability 0.4 and the busy route with probability 0.6. If he chooses the hilly route, the probability that he will be late for work is x and if he chooses the busy route the probability that he will be late for work is 2x. The probability that Benju is late for work on any day is 0.36.

(i)Show that x = 0.225.[2]
(ii)Given that Benju is not late for work, find the probability that he chooses the hilly route.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] 0.4x+0.6 × 2x = 0.36 or 0.4(1-x) +0.6(1 – 2x) = 0.64, a,b terms involving x
[A1] Fully justified by algebra AG 1.6x=0.36 x = 0.225
[M1] Correct numerical numerator of a fraction. Allow unsimplified. P(H|L') = 0.4(1-x) or 0.4 × (1-0.225) or 0.4 × 0.775
[M1] Denominator 0.36 or 0.64. Allow unsimplified. 1-0.36 or 0.64 or 0.4×0.775+0.6×0.55
[A1] 31/64 or 0.484

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 6 Variant 2, question 2.

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