Probability Calculator

Calculate probability of events, combinations, permutations, and conditional probability. Easy-to-use probability tools for statistics.

Single Event Probability

Multiple Events Probability

Probability Formulas

Single Event

P(A) = favorable / total

Example: Rolling a 6 on a die = 1/6 = 0.1667 or 16.67%

AND (Both Events)

P(A and B) = P(A) × P(B)

Example: Two coin flips both heads = 0.5 × 0.5 = 0.25 or 25%

OR (Either Event)

P(A or B) = P(A) + P(B) - P(A and B)

Example: Rolling 5 or 6 = 1/6 + 1/6 = 2/6 = 0.333 or 33.3%

How to Use This Calculator

1

Choose Event Type

Select Single Event for one occurrence, or Multiple Events for calculating AND/OR probabilities.

2

Enter Values

For single events, enter favorable and total outcomes. For multiple events, enter probabilities (0-1) for each event.

3

Select Operation

For multiple events, choose AND if both must occur, or OR if either can occur.

4

View Results

Get probability as decimal, percentage, and odds. Higher values mean more likely to occur.

Example Calculations

Rolling a Die

What's the probability of rolling a 6 on a standard die?

Solution: P = 1/6 = 0.1667 = 16.67%

One favorable outcome out of six possible outcomes.

Drawing a Card

Probability of drawing an ace from a standard deck?

Solution: P = 4/52 = 0.0769 = 7.69%

Four aces in a 52-card deck.

Two Coin Flips

Probability of getting two heads in a row?

Solution: P = 0.5 × 0.5 = 0.25 or 25%

Independent events multiplied together.

Where Probability Is Used

Games & Gambling

Calculate odds in casino games, lotteries, poker, and sports betting. Essential for understanding risk and expected value.

Risk Assessment

Evaluate risks in insurance, finance, and business decisions. Predict likelihood of events and potential outcomes.

Weather Forecasting

Predict weather patterns, precipitation chances, and storm probabilities using statistical models and historical data.

Medical Diagnosis

Calculate disease probability, treatment success rates, and diagnostic test accuracy in healthcare and medicine.

Quality Control

Monitor defect rates, product reliability, and manufacturing consistency using probability-based statistical methods.

Sports Analytics

Predict game outcomes, player performance, and championship probabilities using statistical analysis and modeling.

Frequently Asked Questions

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). It can also be expressed as a percentage (0-100%).

How do you calculate odds?

Odds are calculated as favorable outcomes : unfavorable outcomes. For example, rolling a 6 on a die has odds of 1:5 (one way to win, five ways to lose).

What's the difference between AND and OR probability?

AND probability (multiplication) is when both events must occur. OR probability (addition) is when either event can occur. AND probabilities are always lower than individual probabilities.

Can probability be greater than 1?

No, probability cannot exceed 1 (or 100%). A probability of 1 means the event is certain to occur. Values greater than 1 indicate an error in calculation.

What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It's written as P(A|B) and calculated as P(A and B) / P(B).

How is probability used in real life?

Probability is used in weather forecasting, insurance pricing, medical diagnosis, quality control, sports predictions, financial risk assessment, and many other fields requiring decision-making under uncertainty.