Conditional Probability and its Properties JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : Conditional Probability and its Properties JEE Notes | EduRev

The document Conditional Probability and its Properties JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
All you need of JEE at this link: JEE

Conditional Probability and Multiplication Theorem 

Let A and B be two events such that P(A) > 0. Then P(B|A) denote the conditional probability of B given that A has occurred. Since A is known to have occurred, it becomes the new sample space replacing the original S. From this we led to the definition. Conditional Probability and its Properties JEE Notes | EduRev which is called conditional probability of B given A.

Conditional Probability and its Properties JEE Notes | EduRev = P(A) P(B | A) which is called compound probability or multiplication theorem. It says the probability that both A and B occur is equal to the probability that A occur times the probability that B occurs given that A has occurred.

Note : For any three events A1, A2, A3 we have Conditional Probability and its Properties JEE Notes | EduRev

Ex.1 Two dice are thrown. Find the probability that the numbers appeared has a sum of 8 if it is known that the second dice always exhibits 4.

Sol. Let A be the event of occurrence of 4 always on the second die

= {(1,4), (2, 4), (3, 4) (4,4), (5, 4), (6, 4)} ;              

Conditional Probability and its Properties JEE Notes | EduRev n(A) = 6

and B be the event of occurrence of such numbers on both dice whose sum is 8 = {(4, 4)}.

Thus, A ∩ B = A ∩ {(4, 4)} = {(4, 4)}

Conditional Probability and its Properties JEE Notes | EduRev n(A Ç B) = 1 

Conditional Probability and its Properties JEE Notes | EduRev  Conditional Probability and its Properties JEE Notes | EduRev

 

Ex.2 A bag contains 3 red, 6 white and 7 blue balls. Two balls are drawn one by one. What is the probability that first ball is white and second ball is blue when first drawn ball is not replaced in the bag ?

Sol. Let A be the event of drawing first ball white and B be the event of drawing second ball blue.

Here A and B are dependent events.

P(A) = Conditional Probability and its Properties JEE Notes | EduRev, P (B|A) = Conditional Probability and its Properties JEE Notes | EduRev           

⇒  P(AB) = P(A). P(B/A) = Conditional Probability and its Properties JEE Notes | EduRev


Ex.3:A bag contains 4 red and 4 blue balls. Four balls are drawn one by one from the bag, then find the probability that the drawn balls are in alternate colour.

Sol.  E1 : Event that first drawn ball is red, second is blue and so on.

        E2 : Event that first drawn ball is blue, second is red and so on.

Conditional Probability and its Properties JEE Notes | EduRev P(E1) = Conditional Probability and its Properties JEE Notes | EduRev and

P(E2) = Conditional Probability and its Properties JEE Notes | EduRev     

⇒ P(E) = P(E1) + P(E2) = Conditional Probability and its Properties JEE Notes | EduRev


Ex 4: In a survey in a class, the probability for a person to watch videos is 0.8 and the probability for a person to be a topper, if given that he watches videos is 0.99. find the probability for a person to be both topper and watches videos.
Solution:
let Event E denotes the event that a person watches Examfear videos
let Event F denotes the event that a person is topper
then P(E) = the probability that a person watches Examfear videos =0.8
and P(F|E)= the probability that a person is a topper if he watches Examfear videos=0.99
then P (E ∩ F)= the probability that a person is both topper and also watches Examfear videos
then according to Multiplication Theorem on probability
P (E ∩ F) = P (E) P (F | E)
= 0.8 x 0.99
= 0.792
∴ The probability that a person is both topper and also watches videos = 0.792 

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Extra Questions

,

video lectures

,

Conditional Probability and its Properties JEE Notes | EduRev

,

pdf

,

Important questions

,

shortcuts and tricks

,

practice quizzes

,

Objective type Questions

,

Viva Questions

,

mock tests for examination

,

past year papers

,

ppt

,

Conditional Probability and its Properties JEE Notes | EduRev

,

MCQs

,

Previous Year Questions with Solutions

,

Sample Paper

,

Exam

,

study material

,

Semester Notes

,

Free

,

Summary

,

Conditional Probability and its Properties JEE Notes | EduRev

;