# Probability of at Least n, with probability P, out of N

Discussion in 'Scientific Statistics Math' started by PeterOut, Jun 7, 2008.

1. ### PeterOutGuest

If I randomly select a sample, the probability of it being bad is P.
If I randomly select N samples, what is the probability that at least

Peter.

PeterOut, Jun 7, 2008

2. ### Phil HolmanGuest

This is a binomial distribution
It is going to be easier to use some numbers.
Say P = .4
N = 5
n = 3

For n = 3, p(3) = 5!/(2!*3!)*.4^3*.6^2
For n = 4, p(4) = 5!/(1!*4!)*.4^4*.6^1
For n = 5, p(5) = 5!/(0!*5!)*.4^5*.6^0

The probability for at least 3 to be bad is p(3) + p(4) + p(5).

Phil H

Phil Holman, Jun 7, 2008

3. ### Phil HolmanGuest

P(X=r) = nCr*p^r*(1-p)^(n-r)

where (nCr) = n!/[(n-r)!*r!] ......the number of possible combinations
of r from n.

Phil H

Phil Holman, Jun 7, 2008
4. ### Bruce WeaverGuest

--- snip ---

There is a good binomial distribution calculator at
http://www.stattrek.com/, and probably a tutorial that would be
relevant too.

Bruce Weaver, Jun 7, 2008
5. ### PeterOutGuest

Works great! Thank you for your help.

PeterOut, Jun 12, 2008