A commuter's journey to work consists of driving her car to her local train station, taking a train to the city, and catching a bus to her place of work. If her car trip is delayed she misses the train and is late for work. If the train is delayed, she misses the bus and is late for work. If the bus is delayed she is late for work. The probability that her car journey is delayed is 0.05, the probability that the train is delayed is 0.1, and the probability that the bus is delayed is 0.07.
(a) What is the probability that she arrives at work on time?
(b) What is the probability that she is late for work?
(c) What is the probability that she is late for work because the bus is delayed?