Free Online Probability Calculator for Single and Multiple Events
Probability calculator helps you compute exact probabilities for single events, multiple events (AND/OR), conditional probability, and complementary probability. Get instant results with step-by-step solutions, formulas, and multiple output formats — all free, private, and without any signup.
Calculate Probability Instantly
How to Use the Probability Calculator
Select Calculation Mode
Choose the type of probability calculation you need: Single Event, Multiple Events (AND/OR), Conditional, or Complementary from the mode tabs.
Enter Probability Values
Enter your probability values as decimals (0 to 1), percentages (0% to 100%), or as fractions like favorable outcomes and total outcomes.
Click Calculate Probability
Press the Calculate Probability button or hit Enter to instantly compute results with a detailed step-by-step breakdown of the calculation.
Review Step-by-Step Solution
Review the comprehensive results showing probability as decimal, percentage, fraction, and odds along with the complete solution steps.
Copy or Reset Results
Copy the results to your clipboard for use in assignments, reports, or research, or click Reset to start a new probability calculation.
Key Features of the Probability Calculator
100% Free Forever
Use all probability calculation modes without any cost, signup, or hidden premium features whatsoever.
Precise Accuracy
IEEE 754 double-precision arithmetic ensures results accurate to 15 significant digits matching scientific calculators.
Instant Results
Get probability answers in under 100 milliseconds with step-by-step solutions generated in real time.
Complete Privacy
All calculations run locally in your browser. No data is sent to servers or stored anywhere online.
Mobile Friendly
Fully responsive design works perfectly on smartphones, tablets, and desktop computers of all screen sizes.
No Signup Needed
Start calculating immediately without creating an account, verifying email, or providing personal information.
Probability Formulas and How They Work
P(A) = Favorable Outcomes / Total Outcomes P(A AND B) = P(A) × P(B) [Independent Events] P(A OR B) = P(A) + P(B) − P(A AND B) P(A|B) = P(A ∩ B) / P(B) [Conditional] P(not A) = 1 − P(A) [Complement]Calculation Components
- Single Event Probability: Divides the number of favorable (desired) outcomes by the total number of equally likely outcomes. The result always falls between 0 (impossible) and 1 (certain).
- AND Probability (Intersection): For independent events, multiply individual probabilities. This gives the likelihood that both events occur together simultaneously.
- OR Probability (Union): Add individual probabilities and subtract the intersection to avoid double-counting outcomes that satisfy both events.
- Conditional Probability: Uses Bayes' approach — divides the joint probability P(A∩B) by the probability of the condition P(B) to find how likely A is given B has occurred.
- Complementary Probability: Simply subtracts the event probability from 1. Since an event either happens or doesn't, P(A) + P(not A) always equals 1.
- Odds Conversion: Odds are expressed as favorable-to-unfavorable ratio. If P = 0.25, odds are 1:3 (1 success for every 3 failures).
For instance, if a student in India is preparing for JEE and a question bank has 500 problems with 75 being on probability, the probability of randomly selecting a probability question is P = 75/500 = 0.15 or 15%. This practical application shows how the formula works in everyday academic scenarios that Indian students encounter regularly.
Practical Probability Examples
Dice Roll in a Board Game
Scenario: Ananya in Mumbai is playing Ludo and needs to roll a 6 on a standard die.
Input: Favorable = 1, Total = 6
Result: P = 0.1667 (16.67%) | Odds: 1:5
Use Case: Understanding game probability for strategic decision-making in board games.
Exam Question Selection
Scenario: Rohit preparing for GATE has 200 practice questions; 40 are from his weak topic, Linear Algebra.
Input: Favorable = 40, Total = 200
Result: P = 0.20 (20%) | Odds: 1:4
Use Case: Helps prioritize study topics based on their probability of appearing in exams.
Quality Control in Manufacturing
Scenario: A textile factory in Surat checks products. P(defect in stitching) = 0.05, P(defect in color) = 0.03.
Input: P(A) = 0.05, P(B) = 0.03
P(A AND B) = 0.0015 | P(A OR B) = 0.0785
Use Case: Quality assurance teams calculate combined and individual defect probabilities for production lines.
Medical Test Accuracy (International)
Scenario: A diagnostic test at a London hospital has P(positive AND disease) = 0.09, P(positive result) = 0.12.
Input: P(A∩B) = 0.09, P(B) = 0.12
P(Disease | Positive) = 0.75 (75%)
Use Case: Medical professionals worldwide evaluate test reliability using conditional probability and Bayesian reasoning.
What is a Probability Calculator?
A Probability Calculator is a mathematical tool that computes the likelihood of events occurring based on given outcomes or probability values. Probability is a fundamental concept in mathematics, statistics, data science, and everyday decision-making that quantifies uncertainty on a scale from 0 (impossible) to 1 (certain), often expressed as a percentage from 0% to 100%.
This tool is designed for students preparing for competitive exams like JEE, NEET, CAT, GATE, and board examinations, as well as university students studying statistics and probability theory. Teachers use it to demonstrate probability concepts with real-time calculations in classrooms. Professionals in data science, finance, insurance, quality control, healthcare, and research rely on probability calculations for risk assessment, predictive modeling, and evidence-based decision making.
Our Probability Calculator supports four essential modes: Single Event probability for basic favorable-over-total calculations, Multiple Events for computing AND (intersection) and OR (union) probabilities of independent events, Conditional Probability using the P(A|B) = P(A∩B)/P(B) formula, and Complementary Probability for finding P(not A). Each calculation includes a detailed step-by-step solution with the formula applied, intermediate values, and final results in multiple formats. Built by StoreDropship with guidance from mathematics educators, this tool combines computational accuracy with educational value, making complex probability concepts accessible to learners at every level.