The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific eight-hour day, one defective circuit board was found.
a Find the probability that it was produced during the first hour of operation during that day.
b Find the probability that it was produced during the last hour of operation during that day.
c Given that no defective circuit boards were produced during the first four hours of operation, find the probability that the defective board was manufactured during the fifth hour.