Bernoulli trial

A Bernoulli trial is one random trial with exactly two outcomes, success or failure, and a fixed probability p of success.

A Bernoulli trial is the single-trial building block that the binomial distribution stacks up: one shot, one flip, one yes or no answer. If a player makes 78% of free throws, one attempt is a Bernoulli trial with p=0.78p = 0.78, mean 0.780.78, and standard deviation 0.78(0.22)=0.17160.414\sqrt{0.78(0.22)} = \sqrt{0.1716} \approx 0.414. Counting successes across n=20n = 20 independent attempts turns those trials into a binomial random variable. The trials have to be independent and share the same pp, which is exactly what the binomial setting demands. The idea is squarely AP content, since it is just the binomial setting one trial at a time, but the name Bernoulli is not vocabulary the AP course framework uses.

More random variables and distributions terms, or browse the full statistics glossary.