Calculate basic probability, combined event probability (union, intersection, conditional), and binomial distribution probabilities.
P(A) = Favorable outcomes / Total outcomes
| Property | Value |
|---|---|
| Favorable outcomes | 3 |
| Total outcomes | 10 |
| P(A) | 0.3 = 30% |
| P(not A) = P(A') | 0.7 = 70% |
| Odds for A | 3 : 7 |
| Fraction | 3/10 |
| Rule | Formula |
|---|---|
| Addition rule | P(A∪B) = P(A)+P(B)−P(A∩B) |
| Multiplication (indep.) | P(A∩B) = P(A)·P(B) |
| Conditional | P(A|B) = P(A∩B)/P(B) |
| Complement | P(A') = 1 − P(A) |
| Binomial | C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ |
Calculate probability for single events or combinations of events with our free calculator, covering basic probability, AND (intersection), and OR (union) calculations.
Basic probability = favorable outcomes ÷ total outcomes. For independent events: P(A and B) = P(A) × P(B). For P(A or B) = P(A) + P(B) − P(A and B), avoiding double-counting overlapping outcomes.
Independent events don't affect each other's outcome (like separate coin flips); dependent events do (like drawing cards without replacement), requiring conditional probability for accurate calculation.
Without subtracting the overlap, outcomes where both A and B occur would be counted twice, the subtraction corrects for this double-counting.
No, valid probabilities always fall between 0 (impossible) and 1 (certain), inclusive.
Probability is expressed as a fraction of total outcomes; odds compare favorable to unfavorable outcomes directly (e.g., probability of 1/4 equals odds of 1:3).