Suppose that the number of accidents occurring in an industrial plant is described by a Poisson process with an average of 1.5 accidents every three months. During the last three months, four accidents occurred.
a. Find the probability that no accidents will occur during the current three-month period.
b. Find the probability that fewer accidents will occur during the current three-month period than occurred during the last three-month period.
c. Find the probability that no more than 12 accidents will occur during a particular year.
d. Find the probability that no accidents will occur during a particular year.