Question

To reach the Lancaster University campus from Preston, Peter takes a train, which is scheduled to take 20min, followed by a bus, which is scheduled to take 15min and can be taken if the train is not more than 5min late. The probability that the train arrives more than 5min late is 40%, in which case Peter waits for the next bus, which leaves exactly 30min after the first one. The probability that a bus ride takes at least 20min is 10%, but it never takes more than 30min. Assume that the train and bus times are independent events.

a. The probability that Peter catches the first bus is (rounded to the nearest percent)

b. The probability that Peter arrives to the campus not more than 5min later than according to the schedule is (rounded to the nearest percent):

c. The probability that Peter arrives to the campus at least 35min later than according to the schedule is (rounded to the nearest percent):

Answer 1