Negative Binomial Probability
Chance the k-th success lands on trial n
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Need a fast answer on chance the k-th success lands on trial n? Negative Binomial Probability answers with the steps beside it. Fill in Target Successes (k), Trial Number (n) and Success Probability (0-1) on Negative Binomial Probability and read your answer immediately. Negative Binomial Probability displays each intermediate figure as well. Negative Binomial Probability suits budgeting and planning checks. No account is needed for Negative Binomial Probability. The browser does the arithmetic. Negative Binomial Probability sits in the Math section next to free online negative binomial probability calculator and negative binomial calculator kth success trial probability. Run Negative Binomial Probability twice to find the driving input. Open Negative Binomial Probability and enter your numbers.
What does the Negative Binomial Probability do?
Negative Binomial Probability works out the chance k-th success from the Target Successes, Trial Number, and Success Probability, using Math conventions. With the defaults, negative binomial probability gives chance k-th success of P = 0.25.
- Inputs: Target Successes, Trial Number, and Success Probability.
- Output: the chance k-th success, with the working that produced it.
- Method: standard Math arithmetic for the chance k-th success, computed on the device.
Quick answer
negative binomial probability returns chance k-th success of P = 0.25 with the default inputs (target successes of 2, trial number of 3, success probability of 0.5).
How does the Negative Binomial Probability work?
Negative Binomial Probability computes the chance k-th success directly from your inputs — the Target Successes, Trial Number, and Success Probability feed the formula. The chance k-th success is derived locally, which is why the page still works after the connection drops.
How the Negative Binomial Probability works
Open Negative Binomial Probability, type the Target Successes, Trial Number, and Success Probability you already know, and the output follows in the same breath as the arithmetic that produced it.
How to use it
- Target Successes — the value feeding the negative binomial probability formula directly — match it to your scenario first.
- Trial Number — a core negative binomial probability input applied directly — keep its units consistent with the label.
- Success Probability — one of the values negative binomial probability builds from; the output reflects exactly what you type.
- When the figure from the negative binomial probability calculation differs from your expectation, keep the steps open; they show the exact substitution that produced it.
- Change the Target Successes, Trial Number, and Success Probability you trust least on the negative binomial probability page and compare the two chance k-th success figures; that gap is your margin of error.
The formula behind the result
Where the Math method allows more than one common convention, Negative Binomial Probability uses the one named on the label and computes the result with it from the first term to the last.
Worked example: with target successes of 2, trial number of 3, success probability of 0.5, this negative binomial probability calculation returns P = 0.25. The same run reports Read as: of the first 2 trials, 1 were successes (choose which), then trial 3 succeeds.
The steps it follows:
- Formula: P = C(n−1, k−1) × p^k × (1−p)^(n−k)
- C(2, 1) = 2
- 2 × 0.25 × 0.5 = 0.25
- Counts trials until a quota of successes — the geometric distribution is the k=1 special case
Understanding the result
Work upward from the step list on the negative binomial probability page and stop when the figures stop surprising you; that is the row your error is on.
Where it helps
Negative Binomial Probability fits planning and checking: preparing a quote for a client, testing a case slightly worse than expected, and checking the arithmetic without a spreadsheet, or any moment when the figure needs to be right the first time.
Common mistakes
Skipping the Target Successes, Trial Number, and Success Probability because it looked optional is common, yet on Negative Binomial Probability an empty-looking field still feeds the output.
Tip: Negative Binomial Probability returns P = 0.25 at its defaults; double the Target Successes (k) and it returns Need k ≥ 1, n ≥ k, and p between 0 and 1.
Assumptions and limitations
Results from Negative Binomial Probability are estimates computed from the values entered; real-world outcomes can differ when fees, taxes, or conditions not modeled here apply.
Why use this calculator
Because the steps stay on screen, Negative Binomial Probability doubles as a worked example for anyone learning how the figure is derived.
Frequently Asked Questions
What does negative binomial probability work out?
Underneath the layout, Negative Binomial Probability is one calculation: take the Target Successes, Trial Number, and Success Probability, apply the Math rule, and report the chance k-th success with the substitution visible at each stage. Because nothing is stored server-side, there is no history to clear and no account to close after using Negative Binomial Probability.
How is the chance k-th success worked out on this page?
The first steps are formula: p = c(n−1, k−1) × p^k × (1−p)^(n−k), then c(2, 1) = 2. If a term carries units, Negative Binomial Probability shows where they cancel, and the chance k-th success inherits whatever unit survives the Math expression.
What has to be entered before Negative Binomial Probability produces a result?
The negative binomial probability form needs Target Successes, Trial Number, and Success Probability, and computes the chance k-th success from them.
How much does the Target Successes (k) move the result?
At the defaults Negative Binomial Probability returns P = 0.25; doubling Target Successes (k) to 4 moves it to Need k ≥ 1, n ≥ k, and p between 0 and 1.
What does the result from the Negative Binomial Probability represent?
The main number the negative binomial probability returns is the chance k-th success for your exact inputs. Treat the result from Negative Binomial Probability as a planning figure rather than a binding quote, and confirm important decisions with the relevant professional.
Where does the Negative Binomial Probability fit in day-to-day work?
Students, planners, and professionals reach for Negative Binomial Probability for preparing a quote for a client, testing a case slightly worse than expected, and checking the arithmetic without a spreadsheet, and for sanity-checking numbers that arrived from somewhere else. If the chance k-th success surprises you, change nothing and re-read the labels first; a unit mismatch is far more common than a wrong formula.
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