Probability Calculator – Calculate Event Chances Online
Combine probabilities of one or two independent events.
About the Probability Calculator
What is the Probability Calculator?
A probability calculator combines the probabilities of one or two independent events, including "both", "at least one" and complement outcomes.
Why use this calculator?
From weather forecasts to risk analysis, daily decisions rest on combining small probabilities without double-counting overlaps.
How to use it
- Choose single or two-event mode.
- Enter P(A) and, if needed, P(B) as decimals or percentages.
- Read the combined and complement probabilities.
Formula
P(A∪B) = P(A) + P(B) − P(A)·P(B) for independence.
For dependent events the intersection needs a conditional probability; independence is assumed here.
Frequently Asked Questions
What does "independent" mean?
That one event happening does not change the odds of the other — like two separate coin flips.
Why subtract P(A and B)?
Adding P(A) and P(B) counts the overlap twice. Subtracting it once fixes the double count.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
What is the difference between population and sample?
A population includes every member of a group; a sample is a subset. Sample statistics use n−1 in the denominator to correct for bias.
When should I use median instead of mean?
Use the median when data contains outliers or is skewed, because it is less affected by extreme values than the mean.
What does standard deviation tell me?
It measures how spread out the values are around the mean. A small standard deviation means the data clusters tightly; a large one means it is more scattered.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.