I essentially want to calculate the minimum population size required (number of trials) in order to have say, a 99% chance of achieving 1 success.
If P(y)= (nCy) py qn-y , P(y) in this case is equal to 0.99, y is equal to 1, and p and q are known. So I guess I need to solve for n, when n is not equal to y. Is this easily solveable?
Remember nCy= n when y=1
You will get a non algebraic equation for n which cannot be solved using normal methods. You may have to use an iterative method such as Newton's method - Wikipedia, the free encyclopedia to find n
Thanks Shakarri - I will look into solving this using some form of iteration. Of course, if anyone has any experience solving equations iteratively I would appreciate some tips on where to start, as I've never done this sort of thing before.
Shakarri & WChips Note that nC1 = nC(n-1) = n