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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).

Example

Scenario: Two independent events with 50% and 30% probability, combined with AND.

Result: P(A and B) = 0.5 × 0.3 = 0.15, or 15%.

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.

Frequently Asked Questions

What does 'independent events' mean?
Independent events are ones where the outcome of one has no effect on the probability of the other — like two separate coin flips — as opposed to dependent events like drawing cards from a deck without replacement, where each draw changes the remaining probabilities.
Why subtract P(A)×P(B) for the OR calculation?
Simply adding P(A) and P(B) would double-count the cases where both events happen together, so subtracting the overlap (their product, for independent events) gives the correct combined probability.
Can probability be greater than 100%?
No — probability is always between 0% and 100% by definition; if a calculation produces a result outside that range, it indicates an error in how the events or their independence were modeled.

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