# Thread:

1. ## 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!

2. ## Re: Binomial Probability

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

$\sum\limits_{k = 1}^N {\binom{N}{k}p^k \left( {1 - p} \right)^{N - k} }$

3. ## 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' - ?
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