Question 2201

There is a probability of 710{\frac{7}{10}} that Daniel takes his parents' car to go to school. Otherwise, he will take a bus.

If he takes his parents' car, he has a 150{\frac{1}{50}} probability of being late. The probability that Daniel is late for school given that he took a bus is 120{\frac{1}{20}}.

(a) Find the probability that Daniel arrives to school on time on a randomly chosen day.
(b) Daniel was late for school today. Find the probability he took the bus.

On two randomly chosen days, find the probability that

(c) Daniel was late exactly once,
(d) Daniel took the bus on both days, given that he was late exactly once.
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