CAIE S1 2022 November — Question 1

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2022
SessionNovember
TopicConditional Probability
TypeFinding unknown probability from total probability

1 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 \(2 x\) 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 .
  1. Find the value of \(x\).
  2. Find the probability that, on a randomly chosen day, Kino travels to school by car given that he is not late.