N S Probability Calculator

Example Data Table

Formula Used

This calculator models the number of successes in repeated independent trials.

Exact probability: P(X = s) = C(n, s) × p^s × (1 - p)^{n - s}

At most: P(X ≤ s) = Σ P(X = k), for k = 0 to s

At least: P(X ≥ s) = 1 - P(X ≤ s - 1)

Between: P(a ≤ X ≤ b) = P(X ≤ b) - P(X ≤ a - 1)

Mean: n × p

Variance: n × p × (1 - p)

Standard deviation: √[n × p × (1 - p)]

How to Use This Calculator

1. Enter the total number of trials in the n field.
2. Enter the probability of one success for each trial.
3. Enter the target number of successes in the s field.
4. Select exact, at most, at least, or between mode.
5. Provide an upper value when using the between option.
6. Choose your preferred decimal precision.
7. Press Calculate to show the result above the form.
8. Use the table, graph, CSV, and PDF tools for review.

FAQs

1. What does this calculator measure?

It measures the probability of getting a chosen number of successes across repeated trials when each trial has the same success chance and outcomes are independent.

2. What do n and s represent?

n is the total number of trials. s is the number of successes you want to evaluate for an exact, cumulative, or range-based probability result.

3. When should I use exact probability?

Use exact probability when you need the chance of getting one specific success count, such as exactly 4 successful outcomes in 10 trials.

4. What does at most mean?

At most adds probabilities from zero successes up to your chosen s value. It is useful when lower counts are acceptable or expected.

5. What does at least mean?

At least gives the chance of meeting or exceeding the selected success count. It works well for threshold-based planning and performance checks.

6. Why is the graph helpful?

The graph shows how probability is distributed across all possible success counts. It helps you spot concentration, spread, and likely outcomes quickly.

7. Can I export the results?

Yes. The calculator includes CSV and PDF download options so you can save the summary and probability table for reporting or later review.

8. What assumptions does this method use?

It assumes each trial is independent, the success probability stays constant, and each trial produces only two outcomes: success or failure.