Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 80% of the time because it costs less, and he takes a taxi the other 20% of the time. When taking the subway, he arrives at work on time 70% of the time, whereas he makes it on time 90% of the time when traveling by taxi.
a. What is the probability that Juan took the subway and is at work on time on any given day?
b. What is the probability that Juan took a taxi and is at work on time on any given day?