0 to 1
Enter a decimal between 0 and 1 (e.g. 0.35 = 35%)
Quick:
Ready to calculate
Enter probabilities and click Calculate// compute event, union & intersection probabilities
Calculate single event, union, and intersection probabilities instantly. Free online probability calculator with step-by-step explanations and formulas.
Enter a decimal between 0 and 1 (e.g. 0.35 = 35%)
Ready to calculate
Enter probabilities and click CalculateSelect Single Event, Union, or Intersection from the tabs above.
Input values between 0 and 1 (e.g. 0.35 for 35%). Optionally enter P(A∩B) for joint probability.
Click Calculate to see the result, formula, and step-by-step breakdown.
A probability calculator that computes key probability values for one or two events. Supports single event probability, the union rule P(A∪B) = P(A) + P(B) − P(A∩B), and intersection with conditional probability output P(A|B) and P(B|A).
A probability is a number between 0 and 1 that represents the likelihood of an event occurring. 0 means impossible, 1 means certain. For example, a fair coin flip has P(heads) = 0.5.
P(A∪B) is the probability that event A or event B (or both) occur. It uses the formula: P(A∪B) = P(A) + P(B) − P(A∩B). If the events are mutually exclusive, P(A∩B) = 0.
Two events are independent if the occurrence of one does not affect the other. When independence is assumed, P(A∩B) = P(A) × P(B). This is the default when P(A∩B) is left blank.
P(A∩B) is the probability that both events A and B occur simultaneously. For independent events, it equals P(A) × P(B). If events are not independent, you must provide the actual joint probability.
P(A|B) is the probability of event A occurring given that event B has already occurred. It is calculated as P(A|B) = P(A∩B) / P(B). This tool computes it in Intersection mode.
The complement P(Aᶜ) is the probability that event A does NOT occur. It equals 1 − P(A). For example, if P(rain) = 0.3, then P(no rain) = 0.7. This is shown in Single Event mode.
A probability calculator is a tool that helps you compute the likelihood of events occurring based on mathematical rules. Whether you are studying statistics, working on a data science project, or simply trying to understand the chances of something happening, a probability calculator simplifies the process and shows you the exact formulas involved.
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The most fundamental form of probability involves a single event A. The probability P(A) is expressed as a decimal between 0 (impossible) and 1 (certain). For example, the probability of rolling a 3 on a six-sided die is P(3) = 1/6 ≈ 0.1667. This calculator also shows you the complement P(Aᶜ) = 1 − P(A) and the odds ratio for the event.
The union of two events A and B refers to the probability that at least one of them occurs. The formula for this is the addition rule:
P(A∪B) = P(A) + P(B) − P(A∩B)
The subtraction of P(A∩B) is necessary to avoid counting the overlap twice. If the events are mutually exclusive (they cannot both happen at the same time), then P(A∩B) = 0 and the formula simplifies to P(A∪B) = P(A) + P(B).
For example, drawing either a King or a Heart from a standard deck: P(King) = 4/52, P(Heart) = 13/52, P(King of Hearts) = 1/52. So P(King or Heart) = 4/52 + 13/52 − 1/52 = 16/52 ≈ 0.308.
The intersection of events A and B is the probability that both events occur at the same time. For independent events, this is simply:
P(A∩B) = P(A) × P(B)
For example, if you flip a coin and roll a die, the probability of getting heads AND rolling a 6 is 0.5 × 1/6 ≈ 0.0833.
When events are not independent, you must provide the actual joint probability P(A∩B). This calculator then derives the conditional probabilities P(A|B) and P(B|A) from it.
Conditional probability answers the question: "Given that event B has happened, what is the probability of A?" It is defined as:
P(A|B) = P(A∩B) / P(B)
This is one of the most important concepts in probability and statistics. It is the foundation of Bayes' theorem, which is widely used in machine learning, medical diagnosis, and spam filtering.
Probability calculations are used in virtually every field that involves uncertainty and decision-making:
Always enter probabilities as decimals between 0 and 1. If you have a percentage, divide by 100 first (e.g. 35% = 0.35). When you leave the P(A∩B) field blank, the calculator assumes the events are independent. If you know the events are related (for example, drawing cards without replacement), provide the actual joint probability for a more accurate result.