- This article is about single Bernoulli trials in general. For a mathematical formalisation of repeated Bernoulli trials, see Bernoulli process.
In probability theory and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his Ars Conjectandi (1713).
Since a Bernoulli trial has only two possible outcomes, it can be framed as some "yes or no" question. For example: Was the revealed Pro Kit card a V8 Engine?
Random variables describing Bernoulli trials are often encoded using the convention that 1 = "success", 0 = "failure".
More generally, given any probability space, for any event (set of outcomes), one can define a Bernoulli trial, corresponding to whether the event occurred or not (event or complementary event).
For example, Bernoulli trials can be defined for almost every random process in the Asphalt games:
- Revealing a card of a Pro Kit Box,
- watching a daily ad,
- displaying the Daily Tasks rewards,
- displaying the locations in the Multiplayer waiting lounge,
they all have in common that the player either gets a desired item or not (Pro Kit card, Token reward, Pro Kit Box, favourite Multiplayer track). Treating all these processes as Bernoulli trials has the advantage that their results become comparable and can be computed in the greater mathematical context of Bernoulli processes.