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So far what i know is that r = success, x = trials, x-r = failures, p = probability of success, q = failure. I am confused whether these are correct.

$ P(x=1) ={ \binom{x+r-1}{r-1} ( p^r ) (1-p)^x}$

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The negative binomial distribution is used to measure the probability of k failures before r successes occur.

In your case $r=$success,$x=$trials, $x-r=$failures and $p=$success prob.

So you have $r$ successes and $x-r$ failures and wish to measure the probability for the number of trials required:

$$P(X=x) = \binom{r+(x-r)-1}{r}(p^r)(1-p)^{x-r}$$

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  • $\begingroup$ Thank you for the explanation. $\endgroup$
    – ERON23
    Dec 11 '16 at 1:42

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