# Bayes’ Theorem Calculator

Use Bayes’ Theorem to calculate various probabilities using the calculator below.

## Results:

### Steps to Solve for P(A|B)

#### Bayes' Theorem Formula

P(A|B) = P(B|A) × P(A) / P(B)

#### Substitute Values and Solve

P(A|B) = ? × ? / ?

### Steps to Solve for P(B|A)

#### Bayes' Theorem Formula

P(A|B) = P(B|A) × P(A) / P(B)

#### Rewrite to Solve for P(B|A)

P(B|A) = P(A|B) × P(B) / P(A)

#### Substitute Values and Solve

P(B|A) = ? × ? / ?

### Steps to Solve for P(A)

#### Bayes' Theorem Formula

P(A|B) = P(B|A) × P(A) / P(B)

#### Rewrite to Solve for P(A)

P(A) = P(A|B) × P(B) / P(B|A)

#### Substitute Values and Solve

P(A) = ? × ? / ?

### Steps to Solve for P(B)

#### Bayes' Theorem Formula

P(A|B) = P(B|A) × P(A) / P(B)

#### Rewrite to Solve for P(B)

P(B) = P(B|A) × P(A) / P(A|B)

#### Substitute Values and Solve

P(B) = ? × ? / ?

## On this page:

## How to Calculate Probabilities Using Bayes’ Theorem

In statistics, Bayes’ theorem, also called Bayes’ rule, describes the probability of an event, based on the probabilities of conditions related to the event. It is used to find the conditional probability of an event based on related probabilities.

### Bayes’ Theorem Formula

You can use Bayes’ theorem to calculate the probability of an event given another event given the probability of the event and the probability of the other event. Bayes’ theorem states:

P(A|B) = P(B|A) × P(A) / P(B)

Thus, the probability of event *A* given that event *B* also occurs is equal to the probability of event *B* given that event *A* also occurs times the probability of event *A* divided by the probability of event *B*.

Where:

**P(A)**is the probability of event A happening**P(B)**is the probability of event B happening**P(A|B)**is the probability of event A happening conditional that event B has also happened**P(B|A)**is the probability of event B happening conditional that event A has also happened