Binomial Distribution Calculator
The binomial distribution counts the successes in n independent trials with the same probability p, like heads in 10 coin flips or defective parts in a batch.
How to use it
- Type the number of trials n and the probability of success p.
- Type the number of successes k.
- Read the probabilities of exactly, fewer, at most, more and at least k successes.
Frequently asked questions
What is the binomial formula?
P(X = k) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ. The mean is np and the variance np(1 − p). The cumulative probabilities add these terms; here they are computed with logarithms, so n can go up to 1,000,000.
When can I use the binomial distribution?
When there is a fixed number of trials, each with two outcomes, the same probability of success and independence between trials.
What is the difference between at most and fewer than?
At most k includes k itself, P(X ≤ k); fewer than k does not, P(X < k). In the same way, at least k is P(X ≥ k) and more than k is P(X > k).
🔲 Matrix Calculator
🟰 System of Equations Calculator
🎲 Permutation and Combination Calculator
🎯 Probability Calculator
🔔 Normal Distribution Calculator
ℤ Z-Score Calculator
➗ Long Division Calculator
📊 Standard Deviation Calculator