A-LevelMathematicsProbability and statistics9709/52 · May/June 2021 · Q36 Marks

On each day that Alexa goes to work, the probabilities that she travels by bus, by train or by car are 0.4, 0.35 and 0.25 respectively. When she travels by bus, the probability that she arrives late is 0.55. When she travels by train, the probability that she arrives late is 0.7. When she travels by car, the probability that she arrives late is x. On a randomly chosen day when Alexa goes to work, the probability that she does not arrive late is 0.48.

(a)Find the value of x.[3]
(b)Find the probability that Alexa travels to work by train given that she arrives late.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

M1 0.4×p+0.35×q+0.25×r, p = 0.45, 0.55, q = 0.3, 0.7 and r = (1 - x), x
A1 Linear equation formed using sum of 3 probabilities and 0.48 or 0.52 as appropriate. Accept unsimplified.
A1 Final answer
B1 0.35×0.7 or 0.245 seen as numerator of fraction
M1 P(late) seen as a denominator with their probability as numerator (Accept their p / 0.52 or their p / (0.22 + 0.245 + 0.25×their 0.22))
A1

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