General
Probability Calculator
Calculate basic probability, combined events (AND/OR), binomial distribution, and conditional probability using Bayes' theorem.
Enter values and click Calculate
How is this calculated?
Basic: P = favorable / total
P(A and B): P(A) × P(B) [independent]
P(A or B): P(A) + P(B) − P(A and B)
Binomial: P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
where C(n,k) = n! / (k!(n-k)!)
Bayes: P(A|B) = P(B|A)×P(A) / P(B)
P(B) = P(B|A)×P(A) + P(B|¬A)×P(¬A)FAQ
Frequently asked questions about probability
How do I calculate basic probability?
Divide the number of favorable outcomes by the total number of possible outcomes: P(event) = favorable / total. For example, rolling a 6 on a die: 1/6 ≈ 0.1667 or 16.67%.
What is P(A and B)?
For independent events, P(A and B) = P(A) × P(B). For dependent events, P(A and B) = P(A) × P(B|A). This is the probability both events occur.
What is P(A or B)?
P(A or B) = P(A) + P(B) − P(A and B). For mutually exclusive events where A and B cannot happen together, it simplifies to P(A) + P(B).
What is binomial probability?
The probability of exactly k successes in n independent trials, each with probability p: P(X=k) = C(n,k) × p^k × (1-p)^(n-k). Used for coin flips, pass/fail scenarios.
What is Bayes theorem?
Bayes theorem calculates conditional probability: P(A|B) = P(B|A) × P(A) / P(B). It updates probability estimates given new evidence. Essential in medical testing and spam filtering.
Is this probability calculator free?
Yes, completely free with no sign-up required. All calculations run in your browser — your data stays on your device and is never sent to any server.