Probability Formulas
A compact reference for the probability rules used most often.
Rules
| Rule | Formula |
|---|---|
| Classical probability | P(A) = favorable ÷ total (equally likely outcomes) |
| Complement | P(not A) = 1 − P(A) |
| Addition (any events) | P(A or B) = P(A) + P(B) − P(A and B) |
| Mutually exclusive | P(A or B) = P(A) + P(B) |
| Multiplication (independent) | P(A and B) = P(A) × P(B) |
| Conditional | P(A | B) = P(A and B) ÷ P(B) |
| At least one in n tries | 1 − (1 − p)ⁿ |
Counting
permutations: nPr = n! ÷ (n − r)!
combinations: nCr = n! ÷ (r!(n − r)!)
Example
At least one six in four rolls of a die
- P(no six in one roll) = 5/6
- P(no six in four) = (5/6)⁴ ≈ 0.482
- 1 − 0.482
≈ 0.518, just better than even.