A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2017 · Q57 Marks

Over a period of time Julian finds that on long-distance flights he flies economy class on 82% of flights. On the rest of the flights he flies first class. When he flies economy class, the probability that he gets a good night's sleep is x. When he flies first class, the probability that he gets a good night's sleep is 0.9.

(i)Draw a fully labelled tree diagram to illustrate this situation.[2]
(ii)The probability that Julian gets a good night's sleep on a randomly chosen flight is 0.285. Find the value of x.[2]
(iii)Given that on a particular flight Julian does not get a good night's sleep, find the probability that he is flying economy class.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[1] (i) Must see at least 4 probs correct including one with an x in, correct shape
[1] (i) Shape, clear labels/annotation and all probs correct
[1] (ii) 0.82x + 0.18 × 0.9 = 0.285 (Eqn with x in, two 2-factors on one side)
[1] (ii) x = 0.15
[1] (iii) Attempt at P(E∩not GNS) seen as num or denom of fraction
[1] (iii) Attempt at P(not GNS) seen anywhere
[1] (iii) Correct answer = 0.975

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