Turn two chances into every combined odd.
Enter the probability of two events and see the whole picture: the chance they both happen, that either happens, neither, exactly one, plus the conditional and complement. Or switch to single-event mode for probability and odds from raw outcomes.
Your events
Enter a percent like 30% or a probability like 0.30. Both work.
What the numbers tell you
The two events, drawn to scale
Each circle is sized by its probability; the overlap is P(A and B)
The key probabilities side by side
Outcome scorecard
Every combination, with the formula
Each row shows how the value is built from your two inputs.
| Quantity | Formula | Value |
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Probability, explained
What Is Probability?
Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1 (or 0% to 100%). It is calculated as the number of favorable outcomes divided by the total number of possible outcomes. A probability of 0 means impossible; 1 means certain.
Probability vs Odds
Probability and odds express likelihood differently. Probability is favorable / total (e.g., 3/10 = 0.3). Odds are favorable / unfavorable (e.g., 3:7). To convert probability to odds: odds = p / (1-p). Odds are commonly used in gambling and medical research.
Basic Probability Rules
The complement rule: P(not A) = 1 - P(A). The addition rule for mutually exclusive events: P(A or B) = P(A) + P(B). The multiplication rule for independent events: P(A and B) = P(A) × P(B). These rules form the foundation of probability theory.
Applications of Probability
Probability is used in weather forecasting, insurance risk assessment, medical diagnosis, game theory, machine learning, quality control, and financial modeling. Understanding probability helps you make better decisions under uncertainty and evaluate risks in everyday life.
Common questions
What is the difference between theoretical and experimental probability?
Theoretical probability is calculated from known outcomes (e.g., a fair coin has 0.5 chance of heads). Experimental probability is determined by actual trials (e.g., flipping a coin 100 times and recording results). They converge as the number of trials increases.
Can probability be greater than 1?
No. Probability ranges from 0 to 1 (or 0% to 100%). If your calculation gives a value greater than 1, there is an error in your inputs, favorable outcomes cannot exceed total outcomes.
What does complementary probability mean?
The complementary probability is the probability of an event NOT happening. It equals 1 minus the probability of the event. For example, if P(rain) = 0.3, then P(no rain) = 0.7.
How do I calculate probability for multiple events?
For independent events happening together, multiply their probabilities. For either event happening, add their probabilities (subtracting the overlap for non-mutually exclusive events). This calculator handles single-event probability.
These results assume your inputs are correct probabilities between 0 and 1 (or 0% to 100%). Real-world events are rarely perfectly independent, so treat the independent-event figures as a model, not a guarantee. Verify assumptions before acting on them.