Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 82% of the time because it costs less, and he takes a taxi the other 18% 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 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?

Question

Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 82% of the time because it costs less, and he takes a taxi the other 18% 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 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?