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From what I understand, negative binomial is $P(X=k$ number of trials until $r^{th}$ success)

From this chart,

enter image description here

For the red graph $r = 10$, $P(X=k$ number of trials until $10^{th}$ success)

For all $X<10$, the probability should be $0$ because it is impossible to have less than $10$ trials and get $10$ successes, but the red graph says that there is a chance. Why?

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  • $\begingroup$ Negative binomial models the number of successes before a specified number of failures is achieved. $\endgroup$
    – AlvinL
    Commented Jul 8, 2021 at 6:58
  • $\begingroup$ There are four ways of specifying the negative binomial: number of trials/failures/successes until $r$th success/failure $\endgroup$
    – Henry
    Commented Jul 8, 2021 at 14:58

1 Answer 1

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Usually negative binomial is defined in terms of number of failures until the $r$ successes have been achieved, not the total number of trials.

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