# Conditional Probability Calculator

Calculate P(A given B) from joint probability P(A and B) and condition probability P(B)

> Canonical page: https://elysiatools.com/en/tools/conditional-probability-calculator

- **Category:** Math & Numbers

- **Keywords:** conditional probability, p a given b, joint probability, statistics, probability

## Overview

Calculate conditional probability.

Conditional probability answers: if event B has happened, what is the probability that event A also happened?

Formula: P(A | B) = P(A and B) / P(B).

## Inputs

- **Joint Probability P(A and B)** (number)
- **Condition Probability P(B)** (number)
- **Input Scale** (select)
- **Decimal Places** (number)

## When to use

- Solving statistics homework or academic problems involving basic probability rules.
- Analyzing datasets to find the likelihood of a specific outcome within a filtered subset of data.
- Evaluating risk or forecasting events in business and finance based on prior occurrences.

## How it works

- Enter the joint probability P(A and B), which is the likelihood of both events happening together.
- Input the condition probability P(B), representing the likelihood of the known or prior event.
- Select your preferred input scale (Percent or Proportion) and set the desired decimal precision.
- The calculator divides the joint probability by the condition probability to output the exact conditional probability P(A given B).

## Use cases

- Medical testing: Calculating the probability of a patient actually having a disease given a positive test result.
- Marketing analytics: Determining the likelihood of a customer making a purchase given they clicked on a specific promotional banner.
- Quality control: Finding the probability of a product defect given that it was manufactured on a specific assembly machine.

## Frequently asked questions

### What is conditional probability?

Conditional probability is the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. It is denoted mathematically as P(A | B).

### What is the formula for conditional probability?

The formula is P(A | B) = P(A and B) / P(B), where P(A and B) is the joint probability of both events, and P(B) is the probability of the condition event.

### Can I use percentages instead of decimals?

Yes, the calculator allows you to select either 'Percent' or 'Proportion' as your input scale, automatically handling the mathematical conversions for you.

### What happens if the condition probability P(B) is zero?

If P(B) is zero, the conditional probability is undefined because an event that has a zero percent chance of happening cannot be the given condition.

### What is the difference between joint and conditional probability?

Joint probability measures the likelihood of two events happening at the exact same time. Conditional probability measures the likelihood of one event happening given that the other has already occurred.

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