Combinatorics & Probability Rules
Permutations and combinations with the factorial substitution shown, and the algebra of events — union, intersection, complement, conditional — with the Venn region shaded live. Covers §6.12–6.14 of the statistics material.
Permutations & Combinations
Two-Event Calculator
Enter P(A), P(B), and P(A∩B); every derived probability follows from the rules.
Venn diagram — the selected region is shaded gold; each region is labeled with its probability. FIG. T38-1
Independence is a factual property, not an assumption: A and B are independent exactly when P(A∩B) = P(A)·P(B). Mutually exclusive is different — that means P(A∩B) = 0, which (for nonzero probabilities) makes events strongly dependent.