A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2019 · Q13 Marks

When Shona goes to college she either catches the bus with probability 0.8 or she cycles with probability 0.2. If she catches the bus, the probability that she is late is 0.4. If she cycles, the probability that she is late is x. The probability that Shona is not late for college on a randomly chosen day is 0.63. Find the value of x.

When Shona goes to college she either catches the bus with probability 0.8 or she cycles with probability 0.2. If she catches the bus, the probability that she is late is 0.4. If she cycles, the probability that she is late is x. The probability that Shona is not late for college on a randomly chosen day is 0.63. Find the value of x.[3]

Mark scheme

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

[M1] Equation of form 0.8 × A + 0.2 × B = C, A,B involving 1-x and 0.6 or 0.4 and C = 0.63 or 0.37
[M1] Correct unsimplified equation
[A1]
[M1] Equation of form 0.8 × A + 0.2 × B = C, A,B involving x and 0.6 or 0.4 and C = 0.63 or 0.37
[M1] Correct unsimplified equation
[A1]

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 6 Variant 1, question 1.

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