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Enter your values, then click Calculate result.How this calculator helps
Calculate two-event union, intersection, neither and conditional probabilities using explicit independence or a supplied feasible overlap. Enter zero through one, such as 0.25 for twenty-five percent. The result is displayed as percentages to distinguish the input scale from the output scale. Negative probabilities and values above one are rejected. A chance calculator needs a defined sample space and events; this worksheet cannot decide the probability of an unspecified real-world outcome from a label alone.
How to use it
- 1
Prepare the independently established inputs in the units shown, starting with probabilities as decimals.
- 2
Review inclusive or and the supported scope before submitting; example defaults demonstrate the arithmetic rather than a personal recommendation.
- 3
Click Calculate result to submit the current values. Input edits retain the previous submitted result until you calculate again.
- 4
Read the labeled output with the worked example, then check conditional direction before using the result in another record.
Formula and methodology
P(A∪B)=P(A)+P(B)−P(A∩B). Independent mode uses P(A∩B)=P(A)P(B). P(neither)=1−P(A∪B). P(A|B)=P(A∩B)/P(B).
The calculator applies the displayed arithmetic to the values entered on this device. It does not silently load a local tax rate, currency conversion or commercial assumption.
Worked calculation example
For independent P(A)=0.4 and P(B)=0.3, the intersection is 0.12, inclusive union is 0.58, neither is 0.42 and P(A given B)=0.4. If an independently established intersection is instead 0.1, the union becomes 0.6.
How to interpret your result
For independent P(A)=0.4 and P(B)=0.3, the intersection is 0.12, inclusive union is 0.58, neither is 0.42 and P(A given B)=0.4. If an independently established intersection is instead 0.1, the union becomes 0.6. Two-event probability identities only. Independence is supplied explicitly; no event forecasting, frequency fitting, combinatorial solver or guaranteed chance model. Compare the labeled intermediate outputs with the input units and convention before carrying a number into another worksheet.
For different inputs or formulas, use Binomial Distribution Calculator — Exact and Tail Probabilities; Hypergeometric Calculator; Odds and Risk Ratio Calculator.
Related questions this calculator covers
- probability calculator
- how to calculate probability
- chance calculator
- how to calculate chance
Scenario comparison
| Scenario | What it shows |
|---|---|
| Supplied overlap | 0.4, 0.3 and intersection 0.1 give union 0.6 and neither 0.4. |
| Mutual exclusion | 0.2 and 0.3 with zero overlap give union 0.5. |
| Feasibility check | 0.8 and 0.7 need overlap at least 0.5; a supplied 0.1 is rejected. |
Common mistakes to avoid
- Entering 25 rather than 0.25 for a twenty-five-percent probability.
- Confusing independence with mutual exclusivity.
- Reversing the direction of a conditional probability.
P(A given B) uses B as the conditioning event and divides the overlap by P(B). It is not P(B given A), which usually differs. If P(B)=0, the conditional output is explicitly undefined. When learning how to calculate chance, verify the direction and denominator as carefully as the numerator, especially when interpreting evidence or comparing unequal base rates.
Authoritative reference. Method reference reviewed on 4 October 2026. The displayed worksheet and examples are SolvePilot’s own bounded implementation. The reference does not certify an individual calculation. Review by Mohammad Qasim is editorial and technical, not patient-specific, financial, structural or equipment approval.What can affect the result?
Probabilities as decimals
Enter zero through one, such as 0.25 for twenty-five percent. The result is displayed as percentages to distinguish the input scale from the output scale. Negative probabilities and values above one are rejected. A chance calculator needs a defined sample space and events; this worksheet cannot decide the probability of an unspecified real-world outcome from a label alone.
Inclusive or
The union means A happens, B happens, or both happen. Simply adding the two probabilities double-counts their overlap, so the intersection is subtracted once. Exclusive-or is a different event and is not the main output. When interpreting how to calculate probability, write the event statement first so the operation matches the question rather than selecting a familiar formula by name.
Independence assumption
Independent mode multiplies P(A) and P(B). Choosing it asserts a relationship supplied by the user, not a conclusion discovered by the calculator. Events observed together are not automatically independent. Mutual exclusivity also differs: mutually exclusive events have zero intersection, while independent positive-probability events generally have a nonzero intersection. Use supplied-intersection mode for an independently established overlap.
Feasible overlap
A supplied intersection cannot exceed either event probability and cannot be less than max(0,P(A)+P(B)−1). These bounds ensure union and neither remain valid probabilities. For P(A)=0.8 and P(B)=0.7, overlap must be at least 0.5. The check prevents impossible combinations but does not prove that the supplied values represent a correct real sample space.
Conditional direction
P(A given B) uses B as the conditioning event and divides the overlap by P(B). It is not P(B given A), which usually differs. If P(B)=0, the conditional output is explicitly undefined. When learning how to calculate chance, verify the direction and denominator as carefully as the numerator, especially when interpreting evidence or comparing unequal base rates.
Privacy and browser processing
Values entered on this page are processed in the current browser session. SolvePilot does not require an account and does not receive the values entered into the calculator. Refreshing or closing the page clears the working values unless the browser itself restores a previous session. Avoid entering identifying or account information because the calculation needs summary values only.
Accuracy and verification
Accuracy depends first on input quality. Confirm definitions, scales, dates and source information before entering a value. Keep an independent record of any result used for planning because this page does not create an official statement or retain a calculation history.
Limits of this estimate
Two-event probability identities only. Independence is supplied explicitly; no event forecasting, frequency fitting, combinatorial solver or guaranteed chance model. The entered values are not independently verified. Numerical output does not establish the suitability of its assumptions for a real situation. Calculator inputs are processed locally in the browser interface; avoid entering identifying records and retain the relevant measurement or source basis with any result you save.
Sources and review information
Frequently asked questions
Does or include both events?＋
Yes. The main union output is inclusive, so an outcome where both occur is counted once.
Is independence detected?＋
No. Independent mode uses your explicit assumption; otherwise supply an established intersection.
Can I enter percentages like 25?＋
No. Enter 0.25 for 25 percent. Values must lie between zero and one.
What if the overlap is impossible?＋
Supplied mode rejects an intersection outside the feasible probability bounds.
Why is a conditional result undefined?＋
Conditioning on an event with probability zero gives a zero denominator under this elementary formula.