Bernoulli Trial vs Trial

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 $p = 0.78$, mean $0.78$, and standard deviation $\sqrt{0.78(0.22)} = \sqrt{0.1716} \approx 0.414$. Counting successes across $n = 20$ independent attempts turns those trials into a binomial random variable. The trials have to be independent and share the same $p$, 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.

Trials are the unit you count when you repeat a random process, and they are called independent when the result of one does not change the probabilities for the next. A simulation works by running many trials and tracking how often the event of interest shows up. Flip a coin 20 times and you have run 20 trials, each landing heads or tails; if 12 come up heads the relative frequency of heads is $12/20 = 0.60$. The binomial setting is defined by a fixed number of independent trials that each have the same probability of success.