# Conditional Probability Calculator

## About Conditional Probability Calculator (Formula)

A Conditional Probability Calculator is a tool used in probability theory and statistics to estimate the probability of an event occurring given that another event has already occurred. Conditional probability is used to model situations where the probability of one event depends on the occurrence of another event. The formula used to calculate conditional probability involves the joint probability of the two events and the probability of the given event.

The formula for calculating Conditional Probability (P(A|B)) of event A given event B is:

Conditional Probability (P(A|B)) = P(A ∩ B) / P(B)

Where:

• P(A|B) is the conditional probability of event A occurring given event B has occurred.
• P(A ∩ B) is the joint probability of both events A and B occurring.
• P(B) is the probability of event B occurring.

Using the Conditional Probability Calculator involves these steps:

1. Input: Enter the probabilities of events A and B, as well as the joint probability of events A and B, into the calculator.
2. Calculation: The calculator applies the formula to estimate the conditional probability.
3. Output: The calculator displays the calculated conditional probability.

This tool is particularly useful for statisticians, researchers, and analysts who work with probabilistic models and need to calculate the likelihood of events under specific conditions.

For example, if you want to calculate the probability of a student passing an exam (event A) given that they attended a study group (event B), and you know the joint probability of passing and attending the study group, the Conditional Probability Calculator will help you estimate the conditional probability.

In probability theory, conditional probability is essential for understanding events that are influenced by other events and for making predictions based on partial information.