# Estimate probability from sample frequency in a binomial distribution [duplicate]

If I get $$s$$ successes out of $$n$$ trials in a binomial distribution, what is the probability $$p$$ of getting a success in each individual trial?

Presumably $$p = s/n$$, but what if $$s = 0$$ or $$s = n$$? Would the probability $$p$$ really be $$0$$ or $$1$$?

That seems far too certain if the sample size $$n$$ is very small, so is there some correction factor to account for small sample sizes in estimating $$p$$?

• It depends. What is your loss function, prior distribution, or preferred estimation method?
– whuber
Nov 29, 2018 at 0:05
• Uniform prior distribution in $p$ Nov 29, 2018 at 0:09