1 Answers
In probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. Let E 1 {\displaystyle E_{1}} and E 2 {\displaystyle E_{2}} denote two mutually exclusive events which might occur on a given trial. Then the probability that E 1 {\displaystyle E_{1}} occurs before E 2 {\displaystyle E_{2}} equals the conditional probability that E 1 {\displaystyle E_{1}} occurs given that E 1 {\displaystyle E_{1}} or E 2 {\displaystyle E_{2}} occur on the next trial, which is
The events E 1 {\displaystyle E_{1}} and E 2 {\displaystyle E_{2}} need not be collectively exhaustive.