Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 75% of the time because it costs less, and he takes a taxi the other 25% of the time. When taking the subway, he arrives at work on time 71% of the time, whereas he makes it on time 95% of the time when traveling by taxi. (Give your answers correct to three decimal places.)
(a) What is the probability that Juan took a taxi and is at work on time on any given day?

Question

Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 75% of the time because it costs less, and he takes a taxi the other 25% of the time. When taking the subway, he arrives at work on time 71% of the time, whereas he makes it on time 95% of the time when traveling by taxi. (Give your answers correct to three decimal places.) 
(a) What is the probability that Juan took a taxi and is at work on time on any given day?