The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific seven-hour period, 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.