Probability Calculator

Calculate the likelihood of a single event, two independent events, or convert an odds ratio into probability.

Successful Outcomes

Total Outcomes

Probability

What Is a Probability Calculator?

A Probability Calculator helps you find the chance that an event will happen. It can calculate simple probability, complement probability, two-event probability, independent events, dependent events, conditional probability, and odds conversions.

Probability is used in mathematics, statistics, games, science, finance, business, weather forecasting, risk analysis, and everyday decision-making.

Meaning

What Is Probability?

Probability is a number that shows how likely something is to happen. It can be written as a decimal, fraction, or percentage.

Value	Meaning
$0$	Impossible
$0.5$	Even chance, or 50%
$1$	Certain

Calculator Uses

What This Probability Calculator Can Find

The calculator supports common probability questions and gives results in useful formats.

Single event: Find the chance that one event happens, such as rolling a 6 or getting heads.
Complement probability: Find the chance that an event does not happen, written as P(A').
Two events: Find probabilities such as A and B, A or B, neither event, or exactly one event.
Odds to probability: Convert an odds ratio such as 3:2 into a probability percentage.

The Math

Key Probability Formulas

These are the core rules used by probability calculators.

Basic probability

P(A)=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}

Example: rolling a 6 on a fair die has probability 1 / 6, or about 16.67%.

Complement probability

P(A')=1-P(A)

Example: if there is a 30% chance of rain, the chance of no rain is 70%.

Independent events

P(A\cap B)=P(A)\times P(B)

Use this when one event does not affect the other, such as flipping a coin and rolling a die.

Dependent events

P(A\cap B)=P(A)\times P(B\mid A)

Use this when the first event changes the probability of the second event.

Probability of A or B

P(A\cup B)=P(A)+P(B)-P(A\cap B)

The overlap is subtracted so it is not counted twice.

Advanced Conditions

Advanced Probability Rules

These rules help with conditional probability, neither event, exactly one event, and repeated trials.

Condition	Formula
Conditional probability	$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$
Neither event	$1-P(A\cup B)$
Exactly one event	$P(A)+P(B)-2P(A\cap B)$
At least one success	$1-(1-p)^n$

Formats

Decimal, Fraction, and Percent Probability

A good probability calculator should show results in more than one format so the answer is easy to read.

Format	Example
Decimal	$0.25$
Fraction	$\frac{1}{4}$
Percent	$25\%$

These all represent the same value:

0.25=\frac{1}{4}=25\%

Odds

Odds to Probability Formula

Odds compare successes to failures. Probability compares successes to all possible outcomes.

Odds ratio to probability

\text{Probability}=\frac{\text{Success Odds}}{\text{Success Odds}+\text{Failure Odds}}

Example: odds of 3:2 convert to probability 3 / (3 + 2) = 0.60, or 60%.

Common Questions

Examples of Probability Questions

Probability helps answer everyday questions about chance and risk.

Winning chance: What is the chance of winning a game or drawing a specific card?
Coin flip: What is the probability of getting heads?
Dice roll: What is the chance of rolling a 6?
Two events: What is the probability that A or B happens, or that both events happen?
Risk analysis: What is the likelihood that an unwanted event occurs?

Statistics Help

Frequently Asked Questions

A probability calculator finds the chance that an event will happen. It can calculate simple probability, complement probability, A and B, A or B, independent events, dependent events, and conditional probability.

The basic formula is: Probability = Favorable Outcomes / Total Outcomes.

P(A) means the probability that event A happens.

P(A') means the probability that event A does not happen.

P(A and B) means the probability that both event A and event B happen.

P(A or B) means the probability that event A happens, event B happens, or both events happen.

The formula is: P(A or B) = P(A) + P(B) - P(A and B).

For independent events: P(A and B) = P(A) x P(B).

Conditional probability is the chance of one event happening when another event has already happened. P(A | B) = P(A and B) / P(B).

No. Probability must be between 0 and 1. In percentage form, it must be between 0% and 100%.

A probability of 0 means the event is impossible.

A probability of 1 means the event is certain.

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