Mathematics 9709 · AS & A Level · Probability

Probability — practice question

On any given day, Kino goes to school by bus, by car or on foot with probabilities $0.2$, $0.1$ and $0.7$ respectively. The chance that he is late when he goes by bus is $x$. The chance that he is late when he goes by car is $2x$ and the chance that he is late when he goes on foot is $0.25$. The probability that Kino is late on a randomly selected day is $0.235$.
(a)[3]

Work out the value of $x$.

(b)[2]

Find the probability that Kino travels to school by car on a randomly chosen day, provided that he is not late.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Set up and equate a correct probability expression, for instance $0.2x + 0.1(2x) + 0.7\times0.25 = 0.235$

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