Binomial Distribution Calculator
Exact Binomial Probability P(X = k)
Probability of exactly k successes in n trials
Cumulative Binomial P(X ≤ k)
Probability of at most k successes
Formula
P(X=k) = C(n,k) × pᵏ × (1-p)^(n-k) | Mean = np | Variance = np(1-p)
Frequently Asked Questions
What is the binomial distribution?
The binomial distribution models the number of successes in n independent trials, each with probability p. Examples: number of heads in 10 coin flips, number of defective items in a batch, or passing/failing students on an exam.
What are the conditions for binomial distribution?
Four conditions must hold: (1) Fixed number of trials n, (2) Each trial has exactly two outcomes (success/failure), (3) Probability p is constant across trials, (4) Trials are independent.
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