comparing probability of different size

Question

I have a set of items. Each item has a probability of correctness calculated from no. of correct/no. of attempts. For example item A has 100% of being correct out of the 10 attempts he did. On the other, item B also has 100% of being correct but out of 50 attempts he did. Item C has a 90% of being correct out of the 100 attempts he did. If I have to rank such a set of items, surely item B has a higher rank than item A? And how would one compare item C with the other two? I had been reading on sampling sizes testing e.g. t-tests, but it doesn't seem like the right way to go. Or would it serve if I just add an identical arbitrary number to the denominator when calculating the probability of all the items, to take into account of the number of attempts.

Answer 1

I would construct confidence intervals for each case and compare them one to the other, both in terms of mean, and size.

This is a nice elegant statistical approach that captures both avg and number of experiments in a unified framework.