Question: A small hotel has rooms on only four floors, with four smoke detectors on each floor. Because of improper maintenance, the probability that any one detector is functioning is only 0.55. The probabilities that smoke detectors are functioning are randomly and independently distributed.
a) What is the probability that exactly one smoke detector is working on the top floor?
b) What is the probability that there is exactly one detector working on each of two floors and there are two detectors working on each of the other two floors?