Binomial Probability Calculator
Calculate binomial distribution probabilities.
Find the probability of exactly k successes in n trials with a given success probability.
Binomial Probability
Binomial Probability Formula:
P(X = k) = C(n,k) × p^k × (1-p)^(n-k)
Where:
- n = number of trials
- k = number of successes
- p = probability of success on each trial
- C(n,k) = n! / (k! × (n-k)!) — the binomial coefficient
Conditions for a binomial distribution:
- Fixed number of trials (n)
- Each trial has only two outcomes (success/failure)
- Probability of success (p) is the same for every trial
- Trials are independent
Examples:
- Flipping a coin 10 times: n=10, p=0.5
- Making 20 free throws with 80% accuracy: n=20, p=0.8
- Testing 100 products with 2% defect rate: n=100, p=0.02