# Binomial Probability

• Dec 9th 2012, 07:22 AM
SamanthaJane
Binomial Probability
Hi there,

I am having a few problems with this topic. I am actually not sure if it is on binomial.

I have independent trials - 50. I know the probability of pass and fail.

What I need to find is the probability of AT LEAST a certain number passing.

I cannot get my head around it - I have finally decided it is best to use the nCx formula, but it is impractical to calculate over 30 values individually and sum them.

What is the faster way?

Thanks!
• Dec 9th 2012, 09:03 AM
Plato
Re: Binomial Probability
Quote:

Originally Posted by SamanthaJane
Hi there,
I am having a few problems with this topic. I am actually not sure if it is on binomial. I have independent trials - 50. I know the probability of pass and fail.
What I need to find is the probability of AT LEAST a certain number passing.

If we have $\displaystyle N$ independent trials each of which has probability $\displaystyle p$ and $\displaystyle 0<k\le N$
the probability of AT LEAST $\displaystyle k$successes is:

$\displaystyle \sum\limits_{k = 1}^N {\binom{N}{k}p^k \left( {1 - p} \right)^{N - k} }$
• Dec 9th 2012, 09:13 AM
SamanthaJane
Re: Binomial Probability
Thanks for the response

This is what I have already done, excluding the sum.

I have gotten the answer to the nCx - but how do I go about the sum? I feel like I need to look back at my work on series' - ?