# Binomial in reverse?

• Mar 18th 2013, 06:59 PM
WChips
Binomial in reverse?
Hi,

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?

Cheers,
Chips
• Mar 19th 2013, 06:05 AM
Shakarri
Re: Binomial in reverse?
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
• Mar 19th 2013, 06:11 PM
WChips
Re: Binomial in reverse?
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.
• Mar 19th 2013, 09:11 PM
ibdutt
Re: Binomial in reverse?
Shakarri & WChips Note that nC1 = nC(n-1) = n