7) 3.2.5(180) Recall Problem 3.1.4 where an archer hits a bull’s-eye with a probability of 0.09, and the results of different attempts can be taken to be independent of each other.
(a) If the archer shoots a series of arrows, what is the probability that the first bull’s-eye is scored with the fourth arrow?
(b) What is the probability that the third bull’s-eye is scored with the tenth arrow?
(c) What is the expected number of arrows shot before the first bull’s-eye is scored ?
(d) What is the expected number of arrows shot before the third bull’s-eye is scored ?