Physical Sciences
Four large water pumps supply Bellingham, Washington, with water. If water pump i (i 5 1, 2, 3, 4) breaks down, then the time to repair it has an exponential distribution with l 5 1/(2i) hours. Suppose the water pumps operate independently, and when breakdowns occur, the repair times are also independent.
a. Suppose water pump 1 breaks down. What is the probability that it will take more than 30 minutes to repair?
b. Answer part (a) for water pumps 2, 3, and 4.
c. Suppose all four water pumps break simultaneously. What is the probability that at least one of the four water pumps will not be repaired within one hour?