Probability Calculator
Calculate probability of single events, multiple events, and conditional probability with Venn diagram visualization and step-by-step solutions
Check Probability Calculator
Formula result
Copy-ready result handoff
Use this after calculating single-event, multiple-event, or conditional probability.
Confirm the sample space, event definitions, and independence assumptions.
AND, OR, and conditional formulas depend on whether events overlap or influence each other.
Copy this after replacing the bracketed result with the value shown by the calculator.
Probability result: [paste probability, percent form, odds, and complement]. Inputs checked: Confirm the sample space, event definitions, and independence assumptions. Assumption: AND, OR, and conditional formulas depend on whether events overlap or influence each other. Use case: Class homework, risk check, probability example, or scenario explanation. Next check: Use Combination Calculator when the question is about unordered selections.
Choose single-event, multiple-event, or conditional probability based on the question wording. The result is most reliable when the sample space and independence assumptions are clear before you enter values.
How the result is built
Probability Rules And Worked Example
Use for one event when every outcome in the sample space is equally likely.
Use the subtraction term so overlapping outcomes are not counted twice.
Rolling an even number on a fair die has 3 favorable outcomes out of 6, so P(even) = 3 / 6 = 0.5 = 50%.
- Using the multiplication rule for events that are not independent.
- Counting the same overlapping outcome twice in an OR calculation.
- Entering percentages as whole numbers when the field expects a probability from 0 to 1.
Probability Formulas, Assumptions, And Examples
Calculator Task Context
Use this calculator to compute event probabilities, complements, independent or dependent events, and simple counting-based chances.
Formula And Method Used
The basic model is probability = favorable outcomes / total outcomes, with multiplication and addition rules applied according to the event relationship.
Worked Example
- For drawing one ace from a 52-card deck, favorable outcomes = 4 and total outcomes = 52.
- Probability = 4/52 = 1/13, about 7.69%.
Common Mistakes And Limits
- Do not add probabilities for overlapping events without subtracting the overlap.
- Independent events multiply directly; dependent events require updated totals.
- Probability values must stay between 0 and 1, or 0% and 100%.
Related Calculators
Choosing the right probability mode
Use single-event probability when you know favorable and total outcomes. Use multiple-event probability for AND, OR, and exactly-one questions. Use conditional probability when the wording says one event is already known, such as "given B" or "among the selected group."
Assumptions and limits
Probability values must stay between 0 and 1. Independent-event formulas assume one event does not change the probability of the other. If the problem involves drawing without replacement, changing populations, or hidden bias, define those conditions before using a simple rule.
Related tools
Use the Combination Calculator for unordered selections, the Permutation Calculator for ordered arrangements, and the Statistics Calculator after probability turns into observed data.