Binomial Probability Calculator
Calculate exact probabilities for binomial experiments with our advanced statistical tool
Must be ≥1 integer
Must be ≤n and ≥0
Must be between 0-1
Results
Exact Probability: 0.0000
Cumulative Probability (≤k): 0.0000
Combinations: 0
| Successes | Exact Probability | Cumulative Probability |
|---|
What is Binomial Probability?
Binomial probability calculates the likelihood of achieving exactly k successes in n independent trials with binary outcomes. This statistical method is essential for…
Binomial Probability Formula
The binomial probability formula is:
P(X = k) = C(n,k) × pk × (1-p)n-k
| Variable | Meaning | Range |
|---|---|---|
| n | Number of trials | 1-1000 |
| k | Successes | 0-n |
| p | Success probability | 0-1 |
Practical Examples
Coin Flip Analysis: Calculate probability of getting exactly 5 heads in 10 flips…
How to Use This Calculator
- Enter number of trials
- Specify desired successes
- Input success probability
Key Factors Affecting Binomial Probability
- Trial independence
- Probability consistency
- Sample size
FAQ
Q: Can k be greater than n?
A: No, k must be ≤n