The key difference between a binomial distribution and a negative binomial distribution is that in a binomial distribution, the number of trials is fixed, while in a negative binomial distribution, the number of successes is fixed, meaning we count how many trials are needed to achieve a certain number of successes; essentially, the negative binomial is considered the "inverse" of the binomial distribution
A factory inspector checks items on a production line until they find 3 defective items, where each item checked is a trial and finding a defect is a success.
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