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  "body": "\n## Summary\n\nA Bernoulli trial is a [[random experiment|0HM05N3FJD]] with exactly two possible outcomes, called success and failure.\nThe probability $p$ of success is the same each time the trial is repeated, and the failure has probability $q = 1 - p$.\nA sequence of Bernoulli trials usually means independent repetitions of one trial. The number of successes in $n$ such trials has the [[binomial distribution|0VRWZDWW6B]].\n\n## Remarks\n\nThe outcome of one trial, coded as $1$ for success and $0$ for failure, has the [[Bernoulli distribution|0J97P5KZY0]].\nThe trials are named after Jacob Bernoulli, who studied them in his book Ars Conjectandi of 1713.\nExamples are a coin toss, with heads as success, and a roll of a die, with a six as success and $p = 1/6$.\n\n## Explanations\n\n### L1 human\n\nA Bernoulli trial is a yes-or-no experiment.\nMany questions have this form: does the coin show heads, does the patient recover, does the part fail.\n",
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