Math calculators

Probability calculator

P(A and B), P(A or B) and conditional probability for two events, plus combinations and permutations with or without repetition.

Inputs

P(A)P(B)A and B are

Results

Methodology

Conventions

Probabilities are between 0 and 1. For events that are neither independent nor exclusive, give P(A and B).
Combinations and permutations are counted exactly with whole-number arithmetic.

References

Feller, An Introduction to Probability Theory and Its Applications, vol. 1

Formulas

Union: P(A \cup B) = P(A) + P(B) - P(A \cap B)
Conditional: P(A \mid B) = \frac{P(A \cap B)}{P(B)}
Combinations: \binom{n}{r} = \frac{n!}{r!(n - r)!},\quad \text{with repetition } \binom{n + r - 1}{r}
Permutations: \frac{n!}{(n - r)!},\quad \text{with repetition } n^r