A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2022 · Q15 Marks

On any day, Kino travels to school by bus, by car or on foot with probabilities 0.2, 0.1 and 0.7 respectively. The probability that he is late when he travels by bus is x. The probability that he is late when he travels by car is 2x and the probability that he is late when he travels on foot is 0.25. The probability that, on a randomly chosen day, Kino is late is 0.235.

(a)Find the value of x.[3]
(b)Find the probability that, on a randomly chosen day, Kino travels to school by car given that he is not late.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[M1] 0.2×x+0.1×2x+0.7×0.25 or 0.2x + 0.2x + 0.175 seen.
[M1] Equating their 3 term expression (2 terms involving x) to 0.235
[A1] x=0.15
[M1] 0.1×(1-2×theirx) or 0.1 × 0.7 as numerator and 0.2 × (1 – their x) + 0.1 × (1 – 2 × their x ) + 0.7 × 0.75 with values substituted or 1 - 0.235 or 0.765 as denominator of fraction. Condone 0.2 × (1 – their x) + 0.1 × (1 – × their x) + 0.7 × 0.75 as denominator consistent with 1(a).
[A1] 0.091503267 to at least 3SF. If M0 scored SC B1 for 0.091503267 to at least 3SF.

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.