I am trying to solve a problem involving probabilities.
Suppose there are N1 events and n successes with each success having a probability of p. It is easy to show that the probability of these n events occuring is
N1Cn p^n (1-p)^(N1-n)
What is different about my problem is that rather than varying n I am varying N1.
That is, I want to ask, for example, what range of N1 values can I predict so that I am 95% certain of getting n successes?
As a more specific example, suppose n = 5 and p = 0.3. What is the range of N values which I can be 95% certain that I would get 5 successes? e.g. N = 10 to 30.
Thanks in advance