Binomial Distribution Calculator
Calculate probabilities for binomial distribution scenarios. Enter the number of trials, probability of success, and number of successes to find exact, cumulative, and range probabilities.
How to Use This Calculator
- Number of Trials (n): The total number of independent trials or experiments
- Probability of Success (p): The probability of success on each trial (between 0 and 1)
- Number of Successes (x): The specific number of successes you want to calculate probability for
Understanding the Results
- P(X = x): The probability of getting exactly x successes
- P(X ≤ x): The cumulative probability of getting x or fewer successes
- P(X ≥ x): The probability of getting x or more successes
- Expected Value (μ): The average number of successes expected (n × p)
- Standard Deviation (σ): The measure of variability in the distribution
About Binomial Distribution
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial has the same probability of success. It's commonly used in quality control, medical trials, survey analysis, and many other fields.
The probability mass function is given by: P(X = x) = C(n,x) × p^x × (1-p)^(n-x), where C(n,x) is the binomial coefficient "n choose x".