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High Quality Content by WIKIPEDIA articles! In probability and statistics the negative binomial distribution is a discrete probability distribution. It arises as the probability distribution of the number of failures in a sequence of Bernoulli trials needed to get a specified number of successes. If one throws a die repeatedly until the third time a "1" appears, then the probability distribution of the number of non-"1"s that appear before the third "1" is a negative binomial distribution.