AND and OR probabilities for independent events, with bar visuals.
How to use
- Enter P(A) and P(B) between 0 and 1.
- Choose AND or OR and read the combined probability.
Example
Two fair heads: 0.5 × 0.5 = 0.25.
At least one head: 0.5 + 0.5 − 0.25 = 0.75.
Counting: permutations & combinations; surveys: sample size.
Notes
Dependent events need conditional probability—not this shortcut.
Frequently asked questions
When to use AND vs OR?
AND: P(A)×P(B) if independent. OR: P(A)+P(B)−P(A)×P(B).
Why decimals 0–1?
Enter 50% as 0.5; convert percents by dividing by 100.
What does independent mean?
A does not change B’s probability—e.g. two fair coin flips. Dependent cases need conditional probability.
Why isn’t OR just P(A)+P(B)?
Simultaneous A and B would be double-counted without subtracting P(A)×P(B).
Related calculators?
Counting: permutations. Surveys: sample size.
Can I save my inputs?
Yes. Copy link below the form keeps your current inputs so you can share the scenario or save it for later.