Calculator For Binomial
Calculate binomial probabilities for a given number of trials, success probability, and number of successes. Supports exact, cumulative, and range probabilities.
Published by:
isCalculator Editorial Team
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How to use this tool?
Quick Guide: Binomial Probability Calculator
This calculator computes binomial probabilities for a fixed number of independent trials with two outcomes (success/failure).
Step-by-Step Instructions
- Enter Number of Trials (n): A non-negative integer (e.g., 10).
- Enter Probability of Success (p): A decimal between 0 and 1 (e.g., 0.5 for 50%).
- Choose Calculation Type:
- Exact – Probability of exactly k successes: P(X = k). Enter k in the "Number of Successes" field.
- Cumulative – Probability of at most k successes: P(X ≤ k). Enter k in the same field.
- Range – Probability of successes between two values: P(k₁ ≤ X ≤ k₂). Enter k₁ (From) and k₂ (To).
- Click "Calculate" or press Enter. The result shows as a decimal and percentage.
Important Notes
- All inputs must be non-negative integers except probability (p), which must be between 0 and 1.
- For range calculations, ensure "From" ≤ "To" and "To" ≤ n.
- Results are rounded to 6 decimal places; percentages to 4 decimal places.
Example: n=10, p=0.5, exact k=3 → P(X=3) ≈ 0.1172 (11.7188%).
Previous Results
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Frequently Asked Questions
A binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.
The result is the probability of observing exactly k successes (exact), at most k successes (cumulative), or between k1 and k2 successes (range), given n trials and success probability p.
The calculator validates inputs and shows inline error messages. Ensure n is a non-negative integer, p is between 0 and 1, and k values are non-negative integers within range.
