Binomial Distribution Calculator
Probability Distribution
| k | P(X = k) | P(X ≤ k) |
|---|---|---|
| 0 | 0.10% | 0.10% |
| 1 | 0.98% | 1.07% |
| 2 | 4.39% | 5.47% |
| 3 | 11.72% | 17.19% |
| 4 | 20.51% | 37.70% |
| 5 | 24.61% | 62.30% |
| 6 | 20.51% | 82.81% |
| 7 | 11.72% | 94.53% |
| 8 | 4.39% | 98.93% |
| 9 | 0.98% | 99.90% |
| 10 | 0.10% | 100.00% |
Distribution Summary
The Binomial Distribution Calculator computes probabilities for events with two outcomes (success/failure). It calculates exact and cumulative probabilities, generates distribution charts, and provides key statistics like mean and standard deviation. Perfect for statistics students and researchers.
What Is It?
A binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. This calculator helps visualize and compute:
- Probability of exactly k successes
- Cumulative probabilities
- Distribution shape and statistics
Key Formula
The probability mass function:
P(X = k) = C(n,k) × p^k × (1-p)^(n-k)
Where:
n= number of trialsk= number of successesp= probability of successC(n,k)= combination (n choose k)
How to Use
Enter Parameters:
- Number of trials (n)
- Probability of success (p)
View Results:
- Interactive probability chart
- Complete probability table
- Distribution statistics (mean, variance)
Interpret:
- Hover chart bars for detailed probabilities
- Use table for exact values
- Check summary statistics
FAQs
Q: What’s the maximum number of trials supported?
A: The calculator handles up to 50 trials efficiently while maintaining accuracy.
Q: Can I use decimal probabilities?
A: Yes, enter any probability between 0 and 1 (e.g., 0.25 for 25% chance).
Q: How is cumulative probability calculated?
A: It’s the sum of probabilities for all outcomes up to and including k.
Terminology Explained
Trials (n):
The number of independent experiments or observations.
Probability (p):
The chance of success in a single trial (0 to 1 scale).
Successes (k):
The specific number of positive outcomes you’re evaluating.
PMF:
Probability Mass Function - gives P(X=k).
CDF:
Cumulative Distribution Function - gives P(X≤k).
Expected Value:
The mean of the distribution (n × p).