In probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. Let and denote two mutually exclusive events which might occur on a given trial. Then the probability that occurs before equals the conditional probability that occurs given that or occur on the next trial, which is
The events and need not be collectively exhaustive (if they are, the result is trivial).[1][2]
^Susan Holmes (1998-12-07). "The Craps principle 10/16". statweb.stanford.edu. Retrieved 2016-03-17.
^Jennifer Ouellette (31 August 2010). The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse. Penguin Publishing Group. pp. 50–. ISBN 978-1-101-45903-4.
In probability theory, the crapsprinciple is a theorem about event probabilities under repeated iid trials. Let E 1 {\displaystyle E_{1}} and E 2 {\displaystyle...
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where he excelled at his studies and enjoyed playing chess and shooting craps on the street. He spent many hours reading at The Cooper Union for the Advancement...
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Global Information
![{\displaystyle \operatorname {P} [E_{1}\,\,{\text{before}}\,\,E_{2}]=\operatorname {P} \left[E_{1}\mid E_{1}\cup E_{2}\right]={\frac {\operatorname {P} [E_{1}]}{\operatorname {P} [E_{1}]+\operatorname {P} [E_{2}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1d14b0659b5e40d8140821e6f70f50a03e91326)