Bernoulli trial

A random experiment with exactly two possible outcomes, conventionally called success and failure. Its success probability is fixed for a specified trial.

Probability: A mathematical measure of how likely an event is, expressed on a scale from zero to one. A Bernoulli trial assigns a probability to its success outcome.
Bernoulli distribution: The probability distribution of a binary random variable with success probability p and failure probability 1−p. It gives the probability model for the zero-or-one outcome of a Bernoulli trial.
Coin flipping: A random experiment in which a coin produces heads or tails. A coin flip is a standard trial, with one face designated success.
Multinomial experiment: A fixed number of independent trials, each producing one of several categorical outcomes with constant probabilities. It allows more than two outcome categories, unlike a Bernoulli trial.
Sample space: The set of all possible outcomes of a random experiment. A Bernoulli trial has a sample space containing exactly two outcomes.
Binomial distribution: The distribution of the number of successes in a fixed number of independent trials with the same success probability. It describes the success count when identical Bernoulli trials are repeated independently.
Clinical trial: A research study in which health interventions are evaluated in human participants. A participant's response can sometimes be recorded as a binary endpoint and modeled as a trial outcome.
Categorical distribution: A probability distribution over a finite set of categories, each assigned a probability. It models multiple possible outcomes where the Bernoulli distribution has only two.
Event (probability theory): A set of outcomes from a random experiment to which a probability can be assigned. Success is treated as an event, with all other outcomes grouped as failure.
Geometric distribution: The distribution of the number of independent, equal-probability trials needed to obtain the first success. It uses repeated Bernoulli trials to model waiting until success.

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