This is probably a simple question to most of you but I wasn't seeing a clear solution. I was programming the other day and in one part there is a batch insert into a database of about 30 items at a time. If one member of the batch has an error then the whole batch will fail. I found that about 42% of the batches were indeed failing and wondered how I could use this to detect the actual error rate in the dataset.
I fixed the technical aspects of the problem I was facing but I was wondering how to solve problems like this in general. Abstracted a little it is: if you have sets of x elements (taken at random from the whole dataset) and you know the percent of these sets that have at least one element with a certain property, how can you find roughly the percent of elements in the whole dataset that have that property?