Binomial Probability

Probability of exactly k successes in n independent trials.

P (X = k) = (k n) p^{k} (1 - p)^{n - k}

Variables

Mean $n p$ , variance $n p (1 - p)$ . Requires a fixed number of independent trials with the same success probability.

3 heads in 10 fair coin flips: $(3 10) (0.5)^{10} \approx 0.117$ .

Compute combinations (nCr), permutations (nPr) and factorials with formulas and steps.

Combinations and Permutations

Counting selections (order irrelevant) and arrangements (order matters).

Probability Rules

Addition, complement and multiplication rules.