Edward and his friend cannot go to school when it's sunny outside because they are vampires. Forks, Washington is experiencing a sunny period these days, and there is an 80% chance each day that it will be sunny. Assume that the weather is independent from day to day. Let .V be the number of days until the first day Edward can go outside.
a. What is the probability that Edward will have to wait between 10 to 12 days (inclusive) to go back to school?
b. Given that he has already waited 5 sunny days, what is the probability that his waiting time altogether is between 10 to 12 days (inclusive) to go back to school?
c. What is the expected number of days that he will have to wait to go back to school?