Edward and his friends cannot go outside when it is sunny because they are vampires. Edward's hometown, Forks, Washington is usually very cloudy and rainy, but lately it has been very sunny with an 80% chance that it will be sunny each day for the foreseeable future. Assume that the weather is independent from day to day. Let S denote the number of days until Edward can go outside.
a) What are the distribution and parameters of S?
b) How many days should Edward expect to wait before he can go outside?
c) What is the probability that it is 8 days until Edward can go outside?
d) What is the probability that it takes between 8 and 10 days (inclusive) to go outside?
e) Given that he has already waited through 8 sunny days, what is the probability that his waiting time altogether is between 10 and 12 days (inclusive) to go outside?