Probability Calculator: Events, Odds & Combinations
Calculate basic event probability, combined AND/OR probability for two events, and combinations or permutations (nCr / nPr), all instantly in your browser.
How This Probability Calculator Works
Probability measures how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain), calculated as the number of favorable outcomes divided by the total number of equally likely outcomes. This tool covers the three calculations that come up most often: a single event’s probability (and its odds), the combined probability of two events happening together or either happening, and combinatorics for counting arrangements.
For two events, the correct formula depends on their relationship: independent events (where one occurring doesn’t change the other’s likelihood, like two separate coin flips) use P(A and B) = P(A) × P(B), while mutually exclusive events (which can never both happen, like rolling a 2 or a 5 on a single die) use P(A or B) = P(A) + P(B) with P(A and B) always equal to 0.
The combinations and permutations mode answers a different kind of question: not how likely something is, but how many ways it can happen. Combinations (nCr) count selections where order doesn’t matter, like choosing a 3-person committee from 10 people, while permutations (nPr) count arrangements where order does matter, like awarding 1st, 2nd, and 3rd place among 10 competitors. Both are computed using exact factorial arithmetic via JavaScript’s BigInt, so results stay precise even for larger numbers.
What this tool does
How to use it
Choose a calculation mode
Pick Single Event, Two Events (AND/OR), or Combinations & Permutations depending on what you need.
Enter your values
Fill in the outcome counts, probabilities, or n/r values for your chosen mode.
For two events, pick the relationship
Select whether your two events are independent or mutually exclusive, since the formula differs.
Read the result
The probability, odds, or combination/permutation count appears instantly.
FAQ: Probability Calculator
Divide the number of favorable outcomes by the total number of possible outcomes: P(event) = favorable ÷ total. For example, the probability of rolling a 4 on a standard six-sided die is 1 favorable outcome divided by 6 total outcomes, or about 16.67%.
Independent events don’t affect each other’s probability, like flipping a coin twice, the first flip’s result has no bearing on the second. Mutually exclusive events cannot both happen at the same time, like a single coin flip landing on both heads and tails simultaneously. These are opposite concepts and use different formulas, so mixing them up is a very common probability mistake.
By definition, mutually exclusive events cannot occur together, so the probability of both happening simultaneously is always zero. This is different from independent events, where P(A and B) equals P(A) × P(B), which is generally greater than zero unless one of the individual probabilities is zero.
A combination counts selections where order doesn’t matter (choosing 3 toppings for a pizza, regardless of the order you name them), while a permutation counts arrangements where order does matter (assigning gold, silver, and bronze medals to 3 of 10 racers). Permutations are always greater than or equal to combinations for the same n and r, since every combination can typically be arranged in multiple orders.
Odds for an event are expressed as the ratio of favorable outcomes to unfavorable outcomes (not favorable to total, which is probability), so odds of 1:5 mean 1 favorable outcome for every 5 unfavorable ones. Odds against simply flips that ratio. Odds and probability describe the same underlying likelihood but are conventionally expressed differently, especially in betting contexts.
No, valid probabilities are always between 0 and 1 inclusive (or 0% to 100%), a probability of 0 means the event is impossible and 1 means it’s certain. If a calculation produces a value outside that range, it usually indicates invalid inputs, like probabilities for mutually exclusive events that don’t actually sum to something sensible.