The following is a disscussion problem in our stats class. It seems
that several students arrived at several different answers for part b.
So I am curious if I have made an error and if so, where.
(note: this is exactly how the problem reads.)
A certain experiment is to be performed until a successful result is obtained. The trials are independent and the probability of success on a single trial is 0.25. The costof performing the experiment is $25,000; however, if a failure results, it costs $5,000
to "set-up" for the next trial.
a) What is the expected cost of the project? ans. $40,000
b) Suppose that the experimenter has a maximum of $500,000, what is the probability that the experimental work would cost more than this amount?
here is what i did:
$500,000 - $25,000 = $475,000 (to spend on failures)
$475,000 / $5,000 = 95 failures
X: number of trials
So, we wish to find P ( X > 95 ) = (1-.25)^96 which is approx. 0.