Autobiles pass a point on the highway at a rate of 1 per minute. If 5% of all automobiles are trucks and the arrival process is well approximated as a Poisson process, then answer the following...

Autobiles pass a point on the highway at a rate of 1 per minute. If 5% of all automobiles are trucks and the arrival process is well approximated as a Poisson process, then answer the following questions:

(a) What is the probability that at least one truck passes by during an hour?

(b) Given that 10 trucks have passed by in an hour, what is the expected total number of automobiles that have passed by in that time?

(c) If 50 automobiles have passed by in an hour, what is the probability that 5 of them were trucks?