Probability Calculator
Calculate single and compound event probabilities instantly — P(A), P(A or B), P(A and B), P(not A), conditional probability P(A|B), Bayes' theorem, at-least-one in n trials, and binomial P(X = k). Every result includes the formula, step-by-step solution, percentage, and odds ratio — free, private, and no signup required.
Calculate single and compound event probabilities — P(A), P(A or B), P(A and B), P(not A), conditional probability, Bayes' theorem, and binomial probabilities. All calculations run locally in your browser — no signup required.
Display and convert a single probability
Enter a value between 0 and 1
Why Use Our Probability Calculator?
Instant Probability Calculation
Calculate single event probabilities, complements, unions, intersections, conditional probabilities, Bayes' theorem, and binomial probabilities instantly. The probability calculator covers all fundamental probability rules with step-by-step solutions and a visual probability bar.
Secure Probability Calculator Online
The probability calculator runs entirely client-side in your browser. Your input values are never sent to any server, stored, or tracked — complete privacy for academic, statistical, and professional probability calculations.
Probability Calculator — No Installation
Use the probability calculator directly in any modern browser with no downloads, apps, or plugins required. Switch between 8 calculation modes, see the probability as a percentage and odds ratio, and copy results instantly — 100% free forever.
8 Calculation Modes with Step-by-Step Solutions
The probability calculator covers: single event, complement, union (A or B), intersection (A and B), conditional probability, Bayes' theorem, at-least-one in n trials, and exactly k successes (binomial). Every result includes the formula, step-by-step solution, and odds ratio.
Common Use Cases for Probability Calculator
Statistics & Probability Coursework
Students use the probability calculator to solve homework problems involving compound events, conditional probability, and Bayes' theorem. The step-by-step solution shows the formula and each calculation step — ideal for learning and checking work.
Medical Diagnosis & Screening
Clinicians use Bayes' theorem to update disease probability given a positive test result. The probability calculator's Bayes mode takes prior probability, sensitivity (P(B|A)), and false positive rate (P(B|A')) to compute the posterior probability instantly.
Risk Assessment & Insurance
Risk analysts calculate compound event probabilities for insurance underwriting and risk modeling. The probability calculator handles union and intersection probabilities for correlated and independent risk events with the correct addition and multiplication rules.
Quality Control & Manufacturing
Quality engineers use the binomial probability calculator to determine the probability of exactly k defects in n items, or the probability of at least one defect in a batch. The probability calculator handles both scenarios with exact binomial formulas.
Game Design & Gambling Analysis
Game designers and analysts calculate the probability of winning combinations, streaks, and compound events. The probability calculator converts results to odds ratios (e.g. 3:1) — the format used in gambling and game design.
Machine Learning & Data Science
Data scientists use Bayes' theorem for Naive Bayes classifiers and probabilistic inference. The probability calculator's Bayes mode provides a quick way to verify posterior probability calculations during model development and debugging.
Understanding Probability Calculations
What is Probability?
Probability is a measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). A probability of 0.5 means the event is equally likely to occur or not occur. Our probability calculatorhandles all fundamental probability calculations — from simple single-event probabilities to compound events using the addition rule, multiplication rule, conditional probability, and Bayes' theorem. Results are shown as a decimal probability, percentage, and odds ratio (for : against).
How Our Probability Calculator Works
- Select Calculation Type:Choose from 8 modes — single event, complement, union (A or B), intersection (A and B), conditional probability, Bayes' theorem, at-least-one in n trials, or exactly k successes. The input fields update automatically to show only the values needed for the selected mode.
- Enter Probabilities: Input all probability values as decimals between 0 and 1 (e.g. 0.3 for 30%). The probability calculator validates all inputs — for example, P(A ∩ B) cannot exceed min(P(A), P(B)). All calculations run locally in your browser with no data sent to any server.
- View Results: The probability calculator displays the result as a decimal, percentage, and odds ratio, with a visual probability bar, the formula used, and a step-by-step solution showing every calculation step.
Key Probability Rules
- Complement Rule:P(A') = 1 − P(A). The probability of an event NOT occurring equals 1 minus the probability of it occurring.
- Addition Rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events (P(A ∩ B) = 0), this simplifies to P(A) + P(B).
- Multiplication Rule: P(A ∩ B) = P(A) × P(B) for independent events. For dependent events: P(A ∩ B) = P(A) × P(B|A).
- Bayes' Theorem: P(A|B) = P(B|A) × P(A) / P(B). Used to update the probability of a hypothesis given new evidence — fundamental to Bayesian inference, medical diagnosis, and spam filtering.
Probability vs. Odds
Probability is expressed as a number from 0 to 1 (or 0% to 100%). Oddsexpress the ratio of favorable to unfavorable outcomes. For example, a probability of 0.75 (75%) corresponds to odds of 3:1 (three favorable outcomes for every one unfavorable). The probability calculator automatically converts every result to both formats. Note that “odds” in everyday language (e.g. “3 to 1 odds”) sometimes means the ratio of favorable to total outcomes — always verify which convention is being used.
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Frequently Asked Questions About Probability Calculator
A probability calculator computes the likelihood of events occurring, expressed as a number between 0 and 1. Our probability calculator supports 8 modes including single events, complements, unions, intersections, conditional probability, Bayes' theorem, and binomial probabilities — with step-by-step solutions and runs entirely in your browser.
P(A or B) — written P(A ∪ B) — is the probability that at least one of A or B occurs, calculated as P(A) + P(B) − P(A ∩ B). P(A and B) — written P(A ∩ B) — is the probability that both A and B occur simultaneously. For independent events, P(A ∩ B) = P(A) × P(B).
Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. It is calculated as P(A|B) = P(A ∩ B) / P(B). For example, the probability of drawing a king given the card is a face card is P(king|face card) = (4/52) / (12/52) = 1/3.
Bayes' theorem updates the probability of a hypothesis given new evidence: P(A|B) = P(B|A) × P(A) / P(B). Use it when you have a prior probability P(A), a likelihood P(B|A), and want to find the posterior probability P(A|B). Common applications include medical diagnosis, spam filtering, and machine learning.
The probability of at least one success in n independent trials is P(at least one) = 1 − (1 − P(A))ⁿ. It is easier to calculate the complement (probability of zero successes) and subtract from 1. For example, the probability of at least one head in 3 coin flips = 1 − (0.5)³ = 0.875.
Independent events are events where the occurrence of one does not affect the probability of the other. For independent events, P(A ∩ B) = P(A) × P(B). Dependent events are events where the occurrence of one changes the probability of the other — for these, P(A ∩ B) = P(A) × P(B|A).
Yes. The probability calculator runs 100% locally in your browser. Your input values are never sent to any server, stored in a database, or tracked in any way. Everything stays completely private on your device.
Yes — the probability calculator is 100% free with no signup, no account, and no usage limits. Calculate probabilities as many times as you need, completely free forever. There are no ads, no premium tiers, and no data collection.
To convert probability p to odds (for : against), calculate p / (1 − p). For example, p = 0.75 gives odds of 0.75 / 0.25 = 3:1. The probability calculator automatically shows the odds ratio for every result.