🎲Probability Calculator
Calculate AND, OR, and conditional probabilities for two events, including Bayes' theorem.
Free Probability Calculator
Our free probability calculator handles AND, OR, and conditional probabilities instantly — including Bayes' theorem for reversing a conditional probability. Enter the probabilities of your two events, mark whether they're independent, or supply their joint probability directly, and get every related probability at once.
The joint (AND), the union (OR), and both conditional probabilities are computed together. A Venn diagram shows exactly how the events overlap, and every formula used is shown with your actual numbers substituted in.
Ideal for probability homework, exam prep, or quickly sanity-checking a calculation by hand. No sign-up, no downloads — just clear, accurate probability results.
About the Probability Calculator
Features
AND / OR / conditional
All the standard two-event probability relationships computed at once.
Bayes' theorem
Reverses a conditional probability, with the theorem shown explicitly.
Independent-events toggle
Auto-derives P(A∩B) = P(A)×P(B) when events are independent.
Venn diagram
Visualizes exactly how the two events overlap.
Frequently Asked Questions
What's the difference between AND and OR probability?
P(A AND B) is the chance both events happen; P(A OR B) is the chance at least one happens.
How do I calculate P(A OR B)?
Using P(A) + P(B) − P(A AND B), which avoids double-counting the overlap.
What is conditional probability?
The probability of one event occurring given that another has already occurred, written P(A|B).
What is Bayes' theorem used for?
Reversing a conditional probability — finding P(A|B) when you know P(B|A), P(A), and P(B).
What does "independent events" mean here?
If A and B are independent, knowing one occurred doesn't change the probability of the other, so P(A AND B) simply equals P(A) × P(B).
What if my inputs are inconsistent?
The calculator checks that your joint probability doesn't exceed either individual probability, and flags impossible combinations with an explanation.
Does it show a diagram?
Yes, a Venn diagram visualizes the overlap between your two events.
Does it show the formulas used?
Yes, every probability rule is shown with your specific numbers substituted in.
Is my data stored?
No, everything runs client-side in your browser.
Is it free?
Yes, completely free with no sign-up or limits.