EDUCBA Logo

EDUCBA

MENUMENU
  • Explore
    • EDUCBA Pro
    • PRO Bundles
    • Featured Skills
    • New & Trending
    • Fresh Entries
    • Finance
    • Data Science
    • Programming and Dev
    • Excel
    • Marketing
    • HR
    • PDP
    • VFX and Design
    • Project Management
    • Exam Prep
    • All Courses
  • Blog
  • Enterprise
  • Free Courses
  • Log in
  • Sign Up
Home Finance Finance Resources Finance Formula Conditional Probability Formula
 

Conditional Probability Formula

Madhuri Thakur
Article byMadhuri Thakur

Updated July 24, 2023

Conditional Probability Formula

 

 

Conditional Probability Formula (Table of Contents)
  • Formula
  • Examples

What is the Conditional Probability Formula?

The term “Conditional Probability” refers to the probability of occurrence of one (second ) event, which is dependent on the occurrence of one (first) or more other events.

The formula for conditional probability such that the probability of occurrence of (second) event A given that (first) event B has already occurred can be expressed by dividing the joint probability of events A and B by the probability of occurrence of event B. The joint probability of events A and B is the probability of both events happening simultaneously. Mathematically, conditional probability is represented as,

Watch our Demo Courses and Videos

Valuation, Hadoop, Excel, Mobile Apps, Web Development & many more.

Formula

P(A | B) = P(A ∩ B) / P(B)

Where,

P(A ∩ B): Joint probability of events A and B

P(B): Probability of event B

Example of Conditional Probability Formula (With Excel Template)

Let’s take an example to understand the calculation in a better manner.

You can download this Conditional Probability Formula Excel Template here – Conditional Probability Formula Excel Template

Example #1

Let us take the example of a group of 100 retail buyers, out of which 50 purchased brown bread and 40 purchased peanut butter. However, 30 buyers purchased both brown bread and peanut butter. If a retail buyer selected at random purchased brown bread, what is the probability that he also purchased peanut butter? Also, determine the probability that a randomly chosen buyer has purchased brown bread, given that he also purchased peanut butter.

example of a group

Solution:

Conditional probability is calculated using the formula given below

P(A | B) = P(A ∩ B) / P(B)

Conditional Probability Formula-1.2

  • Conditional probability = 0.30 / 0.50
  • Conditional Probability = 0.60

Conditional probability is calculated using the formula given below

P(B | A) = P(A ∩ B) / P(A)

Conditional Probability Formula-1.3

  • Conditional probability = 0.30 / 0.40
  • Conditional Probability = 0.75

Therefore, if a buyer chosen at random is found to have purchased brown bread, then there is a 60% chance that he has also purchased peanut butter. On the other hand, if a buyer chosen at random has purchased peanut butter, then there is a 75% chance that he has also purchased brown bread.

Example #2

Let us now take the example of a contingency table to illustrate the concept of conditional probability. The contingency table pertains to the probability of boys and girls owning an iPhone. Calculate the following conditional probability:

  • The randomly chosen person in boys that they own an iPhone.
  • The randomly chosen person in girls that they own an iPhone.
  • The randomly chosen person doesn’t own an iPhone, that in boys.
  • The randomly chosen person doesn’t own an iPhone, that in girls.

 contingency table

Solution:

We calculate the conditional probability of boys having an iPhone using the following formula.

P(A | C) = P(A ∩ C) / P(C)

Conditional Probability Formula-2.2

  • Conditional probability = 0.37 / 0.71
  • Conditional Probability = 0.52

The randomly chosen person in boys that own an iPhone = 0.52

The conditional probability that girls have an iPhone is calculated using the formula given below

P(B | C) = P(B ∩ C) / P(C)

own an iPhone

  • Conditional probability = 0.34 / 0.71
  • Conditional Probability = 0.48

The randomly chosen person in girls that they own an iPhone = 0.48

We calculate the conditional probability that boys don’t own an iPhone using the following formula

P(D | A) = P(A ∩ D) / P(A)

Conditional Probability Formula-2.4

  • Conditional probability = 0.12 / 0.49
  • Conditional Probability = 0.24

The randomly chosen person doesn’t own an iPhone, that in boys = 0.24

We calculate the conditional probability that girls don’t own an iPhone using the following formula

P(D | B) = P(B ∩ D) / P(B)

doesn’t own iPhone

  • Conditional probability = 0.17 / 0.51
  • Conditional Probability = 0.33

The randomly chosen person doesn’t own an iPhone, that in girls = 0.33

Explanation

The Conditional Probability Formula can be computed by using the following steps:

Step 1: Firstly, determine the probability of occurrence of the first event B.

Step 2: Next, determine the probability of both events A and B happening together simultaneously. This is the joint probability of events A and B.

Step 3: We can derive the formula for the conditional probability of event A, given that event B has already occurred, by dividing the joint probability of events A and B (step 2) by the probability of event B (step 1), as shown below.

P(A | B) = P(A ∩ B) / P(B)

Relevance and Use

The concept of conditional probability is very important as it has extensive application in many areas, including finance, insurance, and politics. It states the chances of one event only when the other necessary events have already happened. However, it indicates no causal relationship between the first and second events.

Recommended Articles

This is a guide to the Conditional Probability Formula. Here we discuss how to calculate the Conditional Probability Formula along with practical examples. We also provide a downloadable excel template. You may also look aExcel following articles to learn more –

  1. What is a Standard Cost?
  2. How to Calculate Marginal Product?
  3. Calculator of Return on Sales Formula
  4. Calculation of Gross Income

Primary Sidebar

Footer

Follow us!
  • EDUCBA FacebookEDUCBA TwitterEDUCBA LinkedINEDUCBA Instagram
  • EDUCBA YoutubeEDUCBA CourseraEDUCBA Udemy
APPS
EDUCBA Android AppEDUCBA iOS App
Blog
  • Blog
  • Free Tutorials
  • About us
  • Contact us
  • Log in
Courses
  • Enterprise Solutions
  • Free Courses
  • Explore Programs
  • All Courses
  • All in One Bundles
  • Sign up
Email
  • [email protected]

ISO 10004:2018 & ISO 9001:2015 Certified

© 2025 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you
Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you
EDUCBA
Free Investment Banking Course

Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

By continuing above step, you agree to our Terms of Use and Privacy Policy.
*Please provide your correct email id. Login details for this Free course will be emailed to you
EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

EDUCBA

Download Conditional Probability Formula Excel Template

EDUCBA Login

Forgot Password?

EDUCBA

डाउनलोड Conditional Probability Formula Excel Template

🚀 Limited Time Offer! - 🎁 ENROLL NOW