A-LevelMathematicsProbability and statistics9709/53 · May/June 2020 · Q16 Marks

Juan goes to college each day by any one of car or bus or walking. The probability that he goes by car is 0.2, the probability that he goes by bus is 0.45 and the probability that he walks is 0.35. When Juan goes by car, the probability that he arrives early is 0.6. When he goes by bus, the probability that he arrives early is 0.1. When he walks he always arrives early.

(a)Draw a fully labelled tree diagram to represent this information.[2]
(b)Find the probability that Juan goes to college by car given that he arrives early.[4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[B1] Fully correct labelled tree for method of transport with correct probabilities.
[B1] Fully correct labelled branches with correct probabilities for lateness with either 1 branch after W or 2 branches with the probability 0.
[M1] P(C|E) = P(C∩E) / P(E)
[M1] 0.2×0.6 + 0.45×0.1 + 0.35×1
[M1] Summing three appropriate 2-factor probabilities
[A1] 0.12 / 0.515
[A1] 0.233 or 12/515

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.