Independent events
P(A)=40%, P(B)=25%, blank overlapP(A and B)=10%; P(A or B)=55%
Probability Calculator
Use this free probability calculator to find P(A or B), P(A and B), not A, not B, independent-event intersections, formula steps, copy, and history.
Inputs to checkExample numbersCopyable answerTab-only history
Assuming independent eventsP(A or B) = 55%
- P(A and B)
- 10%
- Not A
- 60%
- Not B
- 75%
Steps
- Convert entered percentages to decimals.
- Use P(A and B) = P(A) x P(B).
- Use P(A or B) = P(A) + P(B) - P(A and B).
Recent answers
Recent answers will appear here.
Input tips
Leave P(A and B) blank for independent events.
Enter the intersection when the events overlap in a known way.
How to use the Probability Calculator
- Enter P(A) and P(B) as percentages.
- Leave the intersection blank for independent-event multiplication, or enter P(A and B).
- Press Calculate probability to see union, intersection, complements, and steps.
- Use examples, recent answers, or copy the result while checking probability problems.
What people use it for
Find the chance that A or B happens when you know both event probabilities.
Enter a known overlap when two events can happen together.
Leave the overlap blank when the events are independent.
Calculate complements such as not A and not B.
Catch impossible probability assumptions before copying an answer.
Check classroom probability examples, survey scenarios, and quick planning estimates.
Quick examples
Known overlap
P(A)=60%, P(B)=30%, P(A and B)=15%P(A or B)=75%
Complement
P(A)=40%P(not A)=60%
Mutually exclusive events
P(A)=20%, P(B)=30%, P(A and B)=0%P(A or B)=50%
Large overlap
P(A)=80%, P(B)=70%, P(A and B)=60%P(A or B)=90%
Decimal percentages
P(A)=12.5%, P(B)=20%, blank overlapP(A and B)=2.5%; P(A or B)=30%
Need the guide or a nearby tool?
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- How to use the Probability CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
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Frequently asked questions
Quick answers about formulas, inputs, examples, result copying, and private in-browser history.
What does P(A or B) mean?
P(A or B) is the probability that event A happens, event B happens, or both happen.
What formula does the calculator use for union?
It uses P(A or B) = P(A) + P(B) - P(A and B), so the overlapping part is not counted twice.
What do the main Probability Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Probability Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Probability Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
What happens if I leave P(A and B) blank?
The calculator assumes the events are independent and uses P(A and B) = P(A) x P(B).
When should I enter P(A and B)?
Enter P(A and B) when you already know the overlap, such as the percent of people who fit both groups or the chance that both events happen together.
What are independent events?
Independent events do not change each other. If A happening does not affect B, the calculator can multiply P(A) by P(B) to estimate P(A and B).
What is a complement?
The complement of A is not A. Its probability is 1 - P(A), or 100% minus P(A) when using percentages.
Can I enter decimal percentages?
Yes. You can enter values such as 12.5 or 0.75. The inputs are percentages, so 12.5 means 12.5%, not 0.125%.
Why can the intersection not be larger than A or B?
The overlap cannot include more outcomes than either event by itself. If P(A) is 40%, P(A and B) cannot be 50%.
Can probabilities be more than 100%?
No. Each probability must be between 0% and 100%, and the final union cannot be more than 100%.
Why does the calculator reject some overlaps?
Some entered probabilities contradict each other. For example, if the union would be greater than 100%, at least one input or overlap assumption is not possible.
Can this predict what will happen?
No. It only applies probability formulas to the numbers you enter. Real-world outcomes still depend on whether your assumptions are accurate.
Does this count dice, cards, or combinations for me?
No. First count favorable and total outcomes, then enter the resulting probabilities. Use the Permutation and Combination Calculator when the counting step is the hard part.
Is my probability history private?
Yes. Recent probability answers stay only in the current browser tab while you use the page. They are not sent to a server.