In the rainy season of the region, the occurrence of rain follows a Poisson process with a rate of 3 rainfalls per week. A day with no rainfalls is called a dry day.
(a) (6 pts) What is the probability of having fewer than dry days in a week? (Hint: Use binomial distribution)
(b) (6 pts) Given that a dry day was observed on Saturday, what is the probability that the next dry day will appear on the following Tuesday? (Hint: Use geometric distribution)
(c) (8 pts) Given that a dry day was observed on Saturday, what is the probability that the next Saturday sees the 3rd dry day after the observed one? (Hint: Use a negative binomial distribution)
