Moderate -0.8 This is a straightforward application of Bayes' theorem with clearly stated probabilities and a standard tree diagram structure. The calculation requires finding P(cycles|late) using the law of total probability in the denominator, but all values are given explicitly and the method is routine for S1 students who have practiced conditional probability.
1 When Anya goes to school, the probability that she walks is 0.3 and the probability that she cycles is 0.65 ; if she does not walk or cycle she takes the bus. When Anya walks the probability that she is late is 0.15 . When she cycles the probability that she is late is 0.1 and when she takes the bus the probability that she is late is 0.6 . Given that Anya is late, find the probability that she cycles.
1 When Anya goes to school, the probability that she walks is 0.3 and the probability that she cycles is 0.65 ; if she does not walk or cycle she takes the bus. When Anya walks the probability that she is late is 0.15 . When she cycles the probability that she is late is 0.1 and when she takes the bus the probability that she is late is 0.6 . Given that Anya is late, find the probability that she cycles.
\hfill \mbox{\textit{CAIE S1 2016 Q1 [5]}}