Probability Calculator
Compute single-event, union, and conditional probabilities with standard formulas.
Probability Type
Inputs
Calculator guide
Probability Calculator
The probability calculator covers common event questions, including a single event, the union of two events, and conditional probability. Choose the matching mode and enter probabilities consistently, usually as values from 0 to 1, where 0 means impossible and 1 means certain.
How to use the calculator
- 1Choose the probability operation that matches your problem: a single event, either of two events, or a conditional event.
- 2Enter the known probability values in the requested fields. For a union, include the overlap; for conditional probability, identify the condition event clearly.
- 3Read the result and check whether the assumptions, such as independence, are appropriate for your situation.
Important details to understand
1.Start with the right inputs
Check every number, date, unit, and selected mode before calculating. A correct formula can still give a misleading answer when an input is missing, entered in the wrong unit, or based on a different time period.
2.Know what the calculation includes
The method below describes what this tool uses. Real situations can involve extra rules, costs, calendar conventions, or personal details that are not part of the form, so compare the assumptions with your actual question.
3.Read the unit and rounding
Look at the label as well as the displayed number. Rounding can change the last digits, and results in different units or time periods are not directly comparable until you convert them consistently.
4.Treat the result as a useful check
Use the output to understand a calculation, explore a scenario, or make an initial estimate. When a result affects a formal deadline, a health decision, a contract, or a large payment, confirm it with the relevant source or qualified professional.
How the calculation works
For an event, probability is favorable outcomes divided by total equally likely outcomes. The union formula is P(A∪B)=P(A)+P(B)−P(A∩B). Conditional probability is P(A∩B)÷P(B), provided P(B)>0. Independence is a separate assumption and must not be presumed.
A worked example
If P(A)=0.4, P(B)=0.3, and P(A∩B)=0.1, then P(A∪B)=0.4+0.3−0.1=0.6.
When this calculator is useful
Check introductory probability exercises, reason about overlapping events, or organize known probabilities before applying a formula. Keep track of whether events are mutually exclusive, overlapping, or conditional.
Planning ahead
Try a few realistic input values to see how a change in an amount, measurement, date, or rate affects the answer.
Learning the method
Follow the explanation and example to understand which inputs matter and how they are combined.
Checking your own work
Compare the result with a hand calculation, a worksheet, or a trusted source when you need an independent sense check.
Explaining a result
Keep the original inputs and units with the output so another person can understand what was calculated.
Tips for a more reliable answer
- Enter the values from the same source and keep units consistent throughout the calculation.
- Check that you selected the mode or option that matches the question you are trying to answer.
- Use the worked example to confirm you understand the inputs and the kind of result the tool returns.
- Save the inputs with the result so you can review or repeat the calculation later.
Limitations and assumptions
A numerical output is only as sound as its inputs and assumptions. Events may not be equally likely or independent, and observational data can be biased. This tool does not infer a probability model from raw evidence.
Every result depends on the information entered and the method described above. The calculator cannot confirm that the inputs are complete or that its assumptions match a particular provider, policy, location, body, or real-world situation.
Frequently asked questions
What is the difference between union and intersection?
Union means A or B (or both); intersection means both events happen.
Can probabilities be percentages?
Convert percentages to decimals if the fields expect values from 0 to 1, such as 25% = 0.25.
Does the tool assume events are independent?
No. Use the overlap or conditional information requested by the selected formula.
Why might my result differ from another calculator?
Tools can use different assumptions, units, date conventions, included costs, or rounding rules. Compare the inputs and method descriptions before deciding that one result is wrong.
What should I check if the answer looks wrong?
Review the selected mode, each entered value, the units, and any optional fields. Then compare a simple example with the method described in this guide.
Can I rely on the result for an official or high-impact decision?
Use the result as an estimate or explanation and check the limitations listed for this tool. Confirm important decisions with the relevant official source or a qualified professional.