Probability
Likelihood of outcome.
What does Probability mean?
Probability measures the likelihood that a specific event will occur, expressed as a number between 0 and 1 (or 0% and 100%). A probability of 0 means the event is impossible, while 1 means it is certain. This calculator determines the probability by dividing the number of favorable outcomes by the total number of possible outcomes, and also shows the odds and complementary probability.
How to calculate Probability
Probability is calculated with the formula: P(Event) = Favorable Outcomes / Total Outcomes. For example, if there are 3 favorable outcomes out of 10 total, the probability is 3/10 = 0.3 or 30%. The odds are expressed as 3:7 (favorable to unfavorable). The complementary probability — the chance the event does NOT occur — is 1 − P = 0.7 or 70%.
FAQ
Probability is the ratio of favorable outcomes to total outcomes (e.g., 3/10 = 0.3). Odds compare favorable outcomes to unfavorable outcomes (e.g., 3:7). They convey similar information but in different formats. Odds are commonly used in gambling, while probability is standard in mathematics and science.
No. Probability always ranges from 0 to 1 (or 0% to 100%). A value of 0 means the event is impossible, and 1 means it is certain. If your calculation yields a value greater than 1, check that the number of favorable outcomes does not exceed the total outcomes.
The complementary probability is the chance that an event does NOT occur. It equals 1 minus the probability of the event. For example, if the probability of rain is 30%, the complementary probability (no rain) is 70%. Together, an event and its complement always sum to 100%.
For independent events occurring together, multiply their individual probabilities. For example, the probability of flipping heads twice in a row is 0.5 x 0.5 = 0.25 (25%). For either event occurring, add their probabilities and subtract the overlap: P(A or B) = P(A) + P(B) − P(A and B).
Theoretical probability is calculated using known possible outcomes (e.g., a fair die has a 1/6 chance per face). Experimental probability is based on observed data from actual trials. As the number of trials increases, experimental probability tends to converge toward the theoretical probability — a principle known as the Law of Large Numbers.
Related calculators
- Combinations— Unordered selections.
- Permutations— Ordered arrangements.
- Expected Value— Weighted average outcome.
- Bayes Theorem— Conditional probability update.