9709 P52 - Nov 2022 - Q1
2637
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 \(x\).
(b) Find the probability that, on a randomly chosen day, Kino travels to school by car given that he is not late.
