Mathematics 9709/62 — October/November 2016

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.