Negative Binomial Probability
Chance the k-th success lands on trial n
Negative Binomial Probability is built for chance the k — fast, free, and private. Fill in Target Successes (k), Trial Number (n) and Success Probability (0-1) and read your answer immediately. The result comes with a step-by-step breakdown — no black box, just math you can check. Perfect for budgeting, planning, or checking someone else’s figures. Privacy-first: the calculation is local, your data stays yours, and the tool keeps working offline. Searching for negative binomial calculator kth success trial probability or free online negative binomial probability calculator? This tool covers it — free, fast, and private. No learning curve: the fields are clearly labeled and the result explains itself. Open Negative Binomial Probability, enter your numbers, and you will have a trustworthy answer before you know it.
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, following standard Math conventions — the page defaults produce chance k-th success of P = 0.25.
- Inputs: Target Successes, Trial Number, and Success Probability.
- Output: the chance k-th success, plus the intermediate steps behind it.
- Method: the standard Math formula, evaluated entirely in your browser.
Quick answer
With the default inputs (target successes of 2, trial number of 3, success probability of 0.5), negative binomial probability returns chance k-th success of P = 0.25. Assumptions and limits are summarized below.
How does it 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. Nothing is uploaded: the math runs locally in your browser and the result appears as you type.
How the Negative Binomial Probability works
Negative Binomial Probability turns the values you enter into a verified output — the formula, every intermediate step, and the assumptions sit beside the result instead of hidden behind it.
How to use it
- Target Successes — the value that feeds directly into the formula — match it to the scenario you are modeling before moving on.
- Trial Number — a core input the formula applies directly — keep the units consistent with the label.
- Success Probability — one of the values the calculation builds from; the result reflects exactly what you type here.
- The output panel in negative binomial probability leads with the headline result and follows with the steps behind it, so the value can be checked rather than assumed.
- Explore. Each input change recalculates instantly; watching the chance k-th success move tells you which factor dominates your case.
The formula behind the result
Negative Binomial Probability substitutes the Target Successes, Trial Number, and Success Probability into the formula, evaluates it in the order shown in the steps panel, and reports the result rounded for readability.
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
Substitute your own values and the same steps produce your answer — that is the point of a calculator that shows its working.
Understanding the result
The result panel leads with the chance k-th success and follows with intermediate values; if the headline surprises you, the steps usually reveal which input is responsible.
Where it helps
Common scenarios for Negative Binomial Probability: planning around a target figure, comparing scenarios side by side, and double-checking the chance k-th success. The step list makes it equally useful for learning the method and for double-checking someone else's numbers.
Common mistakes
The most common error with Negative Binomial Probability is a unit mismatch — one value entered in different units than its label assumes quietly skews the output. Check each label before typing.
Tip: Run Negative Binomial Probability twice with deliberately low and high inputs; the spread tells you how sensitive the figure is, which a single run never shows.
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 page doubles as documentation: Negative Binomial Probability puts the formula, a worked example, and the assumptions right beside the calculator.
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Frequently Asked Questions
What does the Negative Binomial Probability calculate?
Negative Binomial Probability answers one question well — given the values you provide, what is the chance k-th success? Enter the Target Successes, Trial Number, and Success Probability, and the result panel returns the value with the full working underneath. Because the working is visible: Negative Binomial Probability shows each operation behind the result in the steps panel, so you can verify the result instead of trusting a black box.
How is the chance k-th success calculated?
The first steps are formula: p = c(n−1, k−1) × p^k × (1−p)^(n−k), then c(2, 1) = 2. The relationship between the inputs is fixed by the formula, and Negative Binomial Probability makes each substitution explicit so nothing about the chance k-th success is hidden.
What do I need to use the Negative Binomial Probability?
The Target Successes, Trial Number, and Success Probability it asks for, or the page defaults if you just want to see the calculation work. Each input maps directly to the formula, and changing any one of them recalculates the chance k-th success instantly.
What does the result from the Negative Binomial Probability mean?
The main number the negative binomial probability returns is the chance k-th success for your exact inputs, and the supporting figures and step list give it context. Negative Binomial Probability assumes the units shown in each label — entering values in different units will skew the result proportionally.
When is the Negative Binomial Probability most useful?
Students, planners, and professionals use it for planning around a target figure, comparing scenarios side by side, and double-checking the chance k-th success, and for sanity-checking numbers that arrived from somewhere else. Bookmark this page — after the first visit it works offline, so the chance k-th success is one tap away even without a connection.