A security consultant has observed that attempts to breach the security of the company's computer system occurs according to a Poisson process with a mean rate of 2.2 attempts per day. (The system is on 24 hours per day.)
(a) What is the probability that there will be 4 breach attempts tomorrow?
(b) What is the probability that there will be no breach attempts during the evening (eight-hour) shift?
(c) It is now midnight and the most recent attempt occured at 10:30PM. What is the probability that the next attempt will occur before 5:30AM?