You randomly call friends who could be potential partners for a dance. You think that they all respond to your requests independently of each other, and you estimate that each one is 7% likely to accept your request. Let X denote the number of calls to successfully get a date.
(a) What are the distribution and parameters of X?
(b) How many calls do you expect to make to get a date?
(c) What is the probability you get a date on the 12th call?
(d) What is the probability it takes you at least 10 calls to get a date?
(e) What is the probability it takes you no more than 15 calls to get a date?
(f) Given you've already called 8 people and still do not have a date, what is the probability it will take less than 14 calls?