Conditional probability, math, Marketing Management

Assignment Help:

What is Conditional Probability?

Two events A and B are said to be dependent when B can occur only when A is known to have occurred (or vice versa). The probability attached to such an event is called the conditional probability and is denoted byP(A/B) or, in other words probability of A given that B has occurred.

If two events A and B are dependent, then the conditional probability of B given A is:

P(B/A) = P(AB)/P(A)

Proof: suppose a1 is the number of cases for the simultaneous happening of A and B out of a1 + a2 cases in which A can happen with or without happening of B.

∴ P(B/A) = a1/(a1 + a2) = (a1/n)/(a1 + a2)/n = P(AB)/P(A)

Similarly it can be shown that

P(A/B) = P[(AB)/P(B)]

The general rule of multiplication in its modified form in terms of conditional probability becomes:

P(A and B) = P(B) × P(A/B)

Or, P(A and B) = P(A) × P(B/A)

For three events A, B and C we have

P(ABC) = P(A) × P(B/A) × P(C/AB)


i.e. the probability of occurrence of A, B and C is equal to the probability of A, times of the probability of B given that A has occurred, times the probability of C given that both A and B have occurred.

Illustration: a bag contains 5 white and 3 black balls. Two balls are drawn at random one after the other without replacement. Find the probability that both balls drawn are black.

Solution: probability of drawing a black ball in the first attempt is

P(A) = 3/(5 + 3) = 3/8

Probability of drawing the second black ball given that the first ball drawn is black

P(B/A) = 2/(5 + 2) = 2/7

∴ The probability that both balls drawn are black is given by

P(AB) = P(A) × P(B/A) = 3/8 × 2/7 = 3/28  

Math Assignment Help


Related Discussions:- Conditional probability, math

1. “Consumer mind is a Black Box” –Discuss, #ques1. “Consumer mind is a Bla...

#ques1. “Consumer mind is a Black Box” –Discusstion..

What are tangible advantages in e-commerce, What are tangible advantages in...

What are tangible advantages in e-commerce? Tangible advantages are as explained below: Through the buyer’s perspective e-commerce gives very many tangible advantages: a.

Probability and combinations, To play a certain lottery, a person has to co...

To play a certain lottery, a person has to correctly select 6 out of 53 numbers, paying $1 for each six-number selection. If the six numbers picked are the same as the ones drawn

Main advantages of keeping an in-house is function, Identify FIVE main adva...

Identify FIVE main advantages of keeping an in-house IS function.   There are several significant advantages of maintaining an in-house IS function, five are listed below. H

Determine the role of market segmentation, Question 1: Determine the ro...

Question 1: Determine the role of market segmentation in effective marketing. Identify and briefly describe the criteria that you would use to help establish whether a variable

Illustrate the the advertising effects on national income, Q. Illustrate th...

Q. Illustrate the the advertising effects on National Income? Effect on National Income: - Advertising increase productive, promotes demand and promotes growth in agriculture

What is advertising standards council of principles, What is Advertising St...

What is Advertising Standards Council of principles? Explain in briefly. Advertising Standards Council of Principles: a) To make sure the truthfulness and honesty of demo

Ford, describe the ford needs to do to make sure its sensitive to change in...

describe the ford needs to do to make sure its sensitive to change in the cultural environment of a country

What is psychographic or psychological segmentation, What is Psychographic ...

What is Psychographic or Psychological Segmentation? Psychographic/Psychological Segmentation: A Psychographic or Psychological characteristic taken as to inner character

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd