Probability Calculator

Permutations count ordered arrangements (order matters). Combinations count unordered selections (order doesn't matter). Example: Choosing 3 from 10 people for roles A, B, C → permutation (P(10,3) = 720). Choosing 3 from 10 for a committee → combination (C(10,3) = 120).

The binomial distribution models the probability of exactly k successes in n independent trials, each with probability p. Formula: P(X=k) = C(n,k) × pᵏ × (1-p)ⁿ⁻ᵏ. Example: flipping a fair coin 10 times, what's the probability of exactly 6 heads?

P(X ≥ k) = 1 − P(X ≤ k−1). P(X ≤ k) = sum of P(X=0) + P(X=1) + ... + P(X=k). This is called the cumulative distribution function (CDF). The calculator shows cumulative probability P(X ≤ k).