
CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
Conditional Probability Formula
The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as Conditional Probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event. This is where the independent event and dependent event notion is used. Consider a student who misses class twice each week, omitting Sunday. What are the possibilities that he will take a leave of absence on Saturday the same week if it is known that he will be absent from school on Tuesday? It has been noted that situations where the outcome of one event influences the outcome of a subsequent event are termed as Conditional Probability.
Quick Links
ToggleWhat Is Conditional Probability Formula?
One of the core concepts in probability theory is the concept of the Conditional Probability Formula. The Conditional Probability Formula calculates the likelihood of an event, say B, given the occurrence of another event, say A.
By knowing the Conditional Probability Formula of event B given that event A has occurred and the individual probabilities of events A and B, the Bayes theorem may be used to calculate the Conditional Probability Formula likelihood of event A given that event B has occurred.
The Conditional Probability Formula of P(A  B) is undefinable if P(B)=0. (Event B did not take place).
Formula for Conditional Probability
The Conditional Probability Formula is as follows:
P(A and B)/P = P(A  B) (B)
Another way to write it is,
P(AB)=P(A∩B)P(B)
Derivation of Conditional Probability Formula
Based on the existence of a prior event or outcome, the Conditional Probability Formula is the likelihood that a future event or outcome will occur. The probability multiplication rule serves as the basis for the Conditional Probability Formula.
P(A) = Chance that event A will occur
P(B) is the likelihood that event B will occur.
P(AB) suggests that both occurrences, A and B, have taken place or at least some of their common components.
Event A is already here.
Every outcome that is not contained in B but is in A is removed if B has also occurred, narrowing the sample space needed to determine B.
The only way that A can occur is when the outcome belongs to the set AB, since the set of possible outcomes for A and B is thus limited to those in which B occurs. As a result, we divide P(A B) by P(B), which is equivalent to limiting the sample space to those instances where B occurs.
Application of Conditional Probability Formula
The Conditional Probability Formula is frequently used to anticipate the results of actions like tossing dice, picking a card from a deck, and flipping a coin. Additionally, it aids in the analysis of the given data set by data scientists, improving results. Creating more precise prediction models is helpful for machine learning developers.
Examples that have been solved to understand the Conditional Probability Formula.
Example 1: Of a group of ten persons, four purchased apples, three purchased oranges, and two purchased both apples and oranges. Using the Conditional Probability Formula, what is the likelihood that a consumer who selected apples at random also purchased oranges?
Solution:
Let those who purchased apples be A and those who purchased oranges be O.
It follows that
P(A) = 4/10, 40%, or 0.4.
P(O) = 3/10, 30%, or 0.3.
Hence,
P(AO) = 2/10, or 20%, or 0.2
Using the Conditional Probability Formula,
50% is equal to P(OA) = P(AO) / P(A) = 0.2 / 0.4 / 0.5
Given that they also purchased apples, there is a 50% chance that the customer also purchased oranges.
Examples Using Conditional Probability Formula
Consider yourself a furniture salesperson. On any given day, 30% of new customers to your business are likely to buy a couch. However, the likelihood may be 70% if they visit your store in the month before the Super Bowl. The Conditional Probability Formula of selling a couch in the month before the Super Bowl may be expressed as P (Selling a couch  Super Bowl month), where the symbol  stands for “given that”. This Conditional Probability Formula gives us a mechanism to define probabilities when our opinions about the likelihood that one event will occur (in this case, the sale of couches) given that another event has occurred change (in this case, the advent of the month preceding the Super Bowl).
FAQs (Frequently Asked Questions)
1. 3 coins are in a piggy bank. 1 fakeheaded coin and 2 regular coins are included. {P (H) = 1 P (H)=1}. A. A person chose a coin at random and tossed it. How likely is it that it will bring up heads?
Based on the supposition,
Assume that A1A1 is the requirement that you choose a regular coin and A2A2 is the requirement that you choose the 2headed coin. A1A1 and A2A2 create a sample space partition, so keep that in mind.
Now,
P(HA1) = 0.5 and P(HA1) = 0.5
P HA2 = 1 P HA2 = 1
Here, using the probability principle, we write
P H P H = P H  A1 P H  A2 P H  A1 – P H  A2 P ‘A1’ plus P ‘HA2’ ‘A2’
1/2.2/3 + 1.1 /3 = 2/3
So the probability obtained is 2/3.