Probability Calculator
Calculate the probability of single and multiple events. Supports independent, mutually exclusive, and dependent events with union, intersection, and complement calculations.
Probability Calculator
Calculate single and multiple event probabilities
Enter a value between 0% and 100%
Enter a value between 0% and 100%
Choose how the two events relate to each other
Your Probability Results
Intersection, union, and complement calculations
Enter the probabilities for Event A and Event B, select their relationship, then click Calculate to see the results.
Common Probability Benchmarks
Quick reference guide for the theoretical probabilities of common random events.
| Event | Probability (Decimal) | Probability (%) | Odds |
|---|---|---|---|
| Coin Toss (Heads) | 0.50 | 50.00% | 1 : 1 |
| 6-Sided Die (Rolling a 6) | 0.1667 | 16.67% | 1 : 5 |
| Deck of Cards (Drawing a Heart) | 0.25 | 25.00% | 1 : 3 |
| Deck of Cards (Drawing an Ace) | 0.0769 | 7.69% | 3 : 49 |
| Two Coins (Both Heads) | 0.25 | 25.00% | 1 : 3 |
| Two Dice (Sum of 7) | 0.1667 | 16.67% | 1 : 5 |
Probability FAQ
Everything you need to know about calculating probabilities, event relationships, and statistical formulas.
Probability is a branch of mathematics that measures the likelihood of an event occurring. It is expressed as a number between 0 and 1 (or 0% and 100%), where 0 means the event is impossible and 1 means the event is certain. The closer the probability is to 1, the more likely the event is to happen.
To calculate the probability of two events (A and B) happening together, also known as the intersection P(A ∩ B), you must know their relationship. If they are independent, you multiply their individual probabilities: P(A) × P(B). If they are mutually exclusive, the probability is 0 because they cannot happen at the same time. If they are dependent, you multiply the probability of A by the conditional probability of B given A: P(A) × P(B|A).
Independent events are events where the outcome of one does not affect the outcome of the other (e.g., flipping a coin and rolling a die). Mutually exclusive events are events that cannot happen at the same time (e.g., flipping a coin and getting both heads and tails on a single flip). For independent events, P(A and B) = P(A) × P(B). For mutually exclusive events, P(A and B) = 0.
Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is denoted as P(B|A), which reads as ‘the probability of B given A’. The formula is P(B|A) = P(A and B) / P(A). This is used for dependent events where the outcome of the first event changes the sample space for the second event, like drawing cards from a deck without replacement.
P(A ∪ B) represents the union of events A and B, which means the probability that either event A occurs, event B occurs, or both occur. The general formula to calculate the union is P(A ∪ B) = P(A) + P(B) – P(A ∩ B). We subtract the intersection to avoid double-counting the scenario where both events happen simultaneously.
No, the probability of a single event can never be greater than 1 (or 100%). A probability of 1 means the event is absolutely certain to happen. If a calculation results in a probability greater than 1, it indicates an error in the input values or the application of the formula, as it violates the fundamental axioms of probability.