Calculator Inputs
The result block appears above this form after submission. The probability table below is limited for readability on large inputs.
Example Data Table
This example assumes 10 trials with a 0.40 success probability. It highlights exact and cumulative probabilities for selected success counts.
| Trials (n) | Success Probability (p) | x | P(X = x) | P(X ≤ x) |
|---|---|---|---|---|
| 10 | 0.40 | 2 | 0.1209 | 0.1673 |
| 10 | 0.40 | 3 | 0.2150 | 0.3823 |
| 10 | 0.40 | 4 | 0.2508 | 0.6331 |
| 10 | 0.40 | 5 | 0.2007 | 0.8338 |
Formula Used
The binomial probability mass function is P(X = x) = C(n, x) × px × (1-p)n-x.
Here, C(n, x) = n! / (x!(n-x)!) counts the number of ways to arrange exactly x successes across n trials.
The cumulative probability is found by summing exact probabilities across a range. For example, P(X ≤ x) equals the sum of all P(X = k) from k = 0 to x.
The calculator also reports the mean np, variance np(1-p), and standard deviation √(np(1-p)).
How to Use This Calculator
- Enter the number of independent trials.
- Enter the success probability as a decimal between 0 and 1.
- Select the probability mode that matches your question.
- Fill in either the single success count or the lower and upper bounds.
- Choose the preferred decimal precision and visible table size.
- Click Calculate Distribution to show results above the form.
- Use the CSV and PDF buttons to save the generated output.