Probability Calculator
Calculate single-event probability, combined probability of two events, or binomial probability — with odds, complements, and a full probability distribution table.
Calculate basic event probability and odds, combine two events using AND/OR/conditional rules, or work out binomial probabilities across a series of independent trials.
How Probability Calculator Works
For a single event, probability is simply favorable outcomes divided by total outcomes: P(A) = favorable/total. The complement, P(not A) = 1 − P(A), and the odds for/against the event are expressed as reduced ratios of favorable to unfavorable outcomes.
For two events, independent events multiply directly: P(A and B) = P(A)×P(B). Mutually exclusive events can never both happen, so P(A and B) = 0 and P(A or B) is just P(A)+P(B). For events that are neither independent nor mutually exclusive, you can enter the known joint probability P(A and B) directly, from which conditional probabilities P(A|B) and P(B|A) are derived by dividing the joint probability by the individual event's probability.
Binomial mode computes the probability of exactly k successes in n independent trials using the binomial probability mass function: P(X=k) = C(n,k) × p^k × (1−p)^(n−k), where C(n,k) counts the number of ways to arrange k successes among n trials. Cumulative probabilities P(X≤k) and P(X≥k) sum this formula across the relevant range of outcomes.
See It In Action
Who Uses Probability Calculator and Why
- Working out the odds of drawing a specific card or rolling a specific outcome for a probability class.
- Combining two independent events, like two separate coin flips, using the multiplication rule.
- Calculating the probability of exactly k successes in n independent trials for a quality-control or genetics problem using the binomial formula.
- Solving a conditional probability question, like P(A|B), for a statistics homework problem.
Mistakes to Avoid
- Multiplying two events' probabilities together as if they're independent when they're actually dependent on each other — this only works for genuinely independent events.
- Confusing 'independent' with 'mutually exclusive' — independent events can both happen and their probabilities multiply, while mutually exclusive events can never both happen and their probabilities simply add for 'or.'
- Applying the binomial formula to trials that don't have a constant probability of success or aren't truly independent of each other.
Tips for Best Results
- Before combining two events, decide whether you need 'and' (multiply, for independent events) or 'or' (add, minus any overlap) — mixing these up is the most common error.
- Use the cumulative P(X≤k) or P(X≥k) binomial results directly rather than manually summing several individual P(X=k) calculations.
Fixing Common Problems
My P(A and B) and P(A or B) results don't seem consistent with each other. — Check whether your two events are actually independent, mutually exclusive, or neither — each case uses a different formula, and applying the wrong one produces inconsistent-looking results.
Terms Explained
Binomial probability: The probability of exactly k successes in n independent trials with a constant success probability p, calculated as C(n,k) × p^k × (1−p)^(n−k).
Conditional probability: The probability of event A occurring given that event B is already known to have occurred, calculated as P(A and B) ÷ P(B).