Probability Calculator
Calculate probabilities for single events, two independent events, or conditional probability.
About Probability
Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). For a single event, P(A) = favorable outcomes / total equally-likely outcomes. Odds express the same information as a ratio: favorable to unfavorable outcomes.
Independent vs. Conditional Events
Two events are independent if knowing the outcome of one tells you nothing about the other. In that case, P(A and B) = P(A) × P(B). For conditional probability, P(A|B) represents the probability of A given that B has already occurred, calculated as P(A∩B) / P(B).
The Addition Rule
For any two events, P(A or B) = P(A) + P(B) − P(A and B). The subtraction avoids double-counting the overlap. For mutually exclusive events (which cannot both occur), P(A and B) = 0, so P(A or B) = P(A) + P(B).
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For a related calculation, use Permutation and Combination Calculator to calculate P(n,r) permutations and C(n,r) combinations with factorial working and Pascal's triangle. Alternatively, use Sample Size Calculator to calculate the required sample size for a given confidence level, expected proportion, and margin of error.
For the underlying method, read A Practical Guide to Statistical Sample Size: How Many People Do You Actually Need to Survey?.