In a binomial distribution if the chance of something happening is p and q=(1-p) and the variance for the event occurring is pq. The variance for the event not occurring is also qp. Since the error within a given confidence interval is related to the variance then this error is the same for both the even occurring and not occurring. In my particular case p=0.1 and with a 95% confidence interval the value of p lies between 0.096 and 0.104 or 0.1+-0.004

I am looking to find the relative error associated with something happening which would be 0.004/0.1= 4%

I want to keep gathering data until the relative error is below 3% but here is what confuses me.

The chance of the event not occurring is 0.9 with the same interval as the chance of it happening (between 0.894 and 0.904 or 0.9+-0.04) and the relative error is 0.004/0.9= 0.44% which is below the 3% I am aiming for.

It does not make sense to be content with the error of the event occurring but not be content with the error of it occurring.

How do people handle relative error in a binomial distribution? Perhaps take an average, or only look at the error in the confidence interval?

- 2 hours ago
- - 4 days left to answer.