How is the negative binomial the inverse of the binomial distribution?

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SUMMARY

The negative binomial distribution is the inverse of the binomial distribution in the context of probability measurements. The binomial distribution calculates the probability of achieving a certain number of successes (X) after a fixed number of trials (n), while the negative binomial distribution determines the number of trials required to achieve a specified number of successes (X). This relationship highlights the conceptual inversion where one focuses on outcomes after trials, and the other on trials needed for outcomes.

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Simfish
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Can anyone give a user-friendly explanation?

http://en.wikipedia.org/wiki/Negative_binomial_distribution#Properties

We see that the binomial distribution measures the probability of X successes after n trials, whereas the negative binomial measures the probability of the trial number after the Xth success. The question is - how does this relate to an inverse? How would the word "inverse" simplify the analogy?
 
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It is not an inverse in the usual sense that g-1(g(x)) = x.
 

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