Conditional probability, math, Marketing Management

Assignment Help:

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 


Related Discussions:- Conditional probability, math

Requirements of a good marketing information system, Requirements of a good...

Requirements of a good marketing information system: 1.       Through there will be a several information component and activity component of a marketing information system yet

General marketing and marketing budget, 1. General Admin costs cover the ge...

1. General Admin costs cover the general running of the organisation. It includes rates, electricity and maintenance recovered from Council - see Income. 2. The high cost of a

Matrices, [1 - x] -4 [2 -2] [3z 10] [2y -3] [0 3] = [4 -u]

[1 - x] -4 [2 -2] [3z 10] [2y -3] [0 3] = [4 -u]

Role of source help the organization, Role of source help the organization ...

Role of source help the organization in following manner: 1) Source communication the communication to the target audience. He is the person who starts the communication proces

What are various perspectives to explain e-commerce, What are various persp...

What are various perspectives to explain E-Commerce? E-Commerce can be defined through various perspectives, which are given below: a. Communications perspective b. Bus

Marketing plan, Marketing plan for a "global" Airline company that is local...

Marketing plan for a "global" Airline company that is localising the global. e.g. Lufhtansa in nigeria

Importance of people and knowledge in an organization, Question: "Your ...

Question: "Your most precious possession is not your financial assets. Your most precious possession is the people you have working there, and what they carry around in their h

Explain aid of a market model , Read the article entitled 'Easter egg price...

Read the article entitled 'Easter egg prices rise by around 5 per cent over last year' and answer questions 1, 2 and 3. Easter egg prices rise by around 5 per cent over last year C

What is test marketing strategy development, What is Concept Testing Strate...

What is Concept Testing Strategy Development? Test Marketing: Throughout this stage the product is in fact tried out in selected Market Segments only based upon the result

Target market, The first five years of operation target marketare people ag...

The first five years of operation target marketare people aged between (2- 67) years old. The demographic age of KualaLumpur population shows that: 0-14years:   29.6%(male4

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