A local public-action group solicits donations by telephone. For a particular list of prospects it was estimated that for any individual the probability was 0.05 of an immediate donation by credit card, 0.25 of no immediate donation but a request for further information through the mail, and 0.7 of no expression of interest. Information is mailed to all people requesting it, and it is estimated that 20% of these people will eventually donate. An operator makes a sequence of calls, the outcomes of which can be assumed to be independent.
a. What is the probability that no immediate credit card donation will be received until at least four unsuccessful calls have been made?
b. What is the probability that the first call leading to any donation (either immediately or eventually after a mailing) is preceded by at least four unsuccessful calls?