1. Airline passengers arrive randomly and independently at the passenger-screening facility
at a major international airport. The mean arrival rate is 10 passengers per minute.
a) Compute the probability of no arrivals in a one-minute period.
b) Compute the probability that three or fewer passengers arrive in a one-minute period.
c) Compute the probability of no arrivals in a 15-second period.
d) Compute the probability of at least one arrival in a 15-second period.
The probability that an automobile being filled with gasoline also needs an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.10. (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?