The negative binomial can be applied in any situation in which there is a series of independent trials, each of which can result in either of just two outcomes. The distribution applies to the number of trials that occur before the designated outcome occurs.
For example, if you start flipping a fair coin repeatedly the negative binomial distribution gives the number of times you must flip the coin until you see 'heads'.
There are also 'everyday' applications in inventory control and the insurance industry.
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Everyday life is frequently irrational.
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Unless your "everyday life" involves work in some area of engineering, you won't use matrices in your everyday life.