Probability Calculator
Calculate the probability of a single event, or the combined probability of two events with AND/OR logic.
About the Probability Calculator
Combining probabilities correctly depends entirely on whether you need both events to happen (AND) or either one to happen (OR) — the two calculations use different formulas and give very different answers. This calculator handles a single event's probability, or the combined probability under either rule.
How It Works
For a single event, the calculator simply returns the probability you entered. For "AND" (assuming independent events), it multiplies the two probabilities together. For "OR", it adds the two probabilities and subtracts their product to avoid double-counting the overlap where both events occur together.
AND (independent events): P(A and B) = P(A) × P(B). OR: P(A or B) = P(A) + P(B) − P(A) × P(B).
Worked example
Scenario: Two independent events: A has a 50% chance and B a 30% chance. What's the chance both happen?
- Convert to decimals: 0.5 and 0.3.
- Both (A and B): 0.5 × 0.3 = 0.15 = 15%.
- Either (A or B): 0.5 + 0.3 − 0.15 = 0.65 = 65%.
Result: 15% that both happen; 65% that at least one happens.
How to interpret probability
Probability ranges from 0 to 1, or from 0% to 100%. A probability of 0 means an event is impossible under the stated assumptions; 1 means it is certain. For independent events, “A and B” uses multiplication. “A or B” requires care: if the events can overlap, the overlap must be subtracted so it is not counted twice.
Tips and common mistakes
- 'And' and 'or' here assume the events are independent — one doesn't affect the other.
- For events that can't happen together (like rolling a 1 or a 2 on one die), add the probabilities instead.
- Probabilities must be between 0% and 100%.
Assumptions & Limitations
- AND and OR calculations assume the two events are statistically independent — the outcome of one does not affect the other.
- For dependent events, these formulas would need to be adjusted with conditional probabilities, which this simplified calculator does not compute.
- Does not handle conditional probability, Bayesian updates, or dependent event scenarios — those require more advanced probability tools.