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

How should marketing deliver value, How should marketing deliver value? ...

How should marketing deliver value? It is the nature of marketing. Marketer has to track customer requirements and deliver the product as per their needs. The company should sa

Companys marketing audit process, Question 1: You are a marketing assi...

Question 1: You are a marketing assistant for a manufacturer of a branded range of household cleaning products: (a) Describe key factors that could be taken into account wh

Caselet, 1.Considering the concept of product life cycle, where would you p...

1.Considering the concept of product life cycle, where would you put video games in their life cycle? 2. Should video game companies continue to alter their products to include oth

Find out fncs, Given the locations of mesh routers and their traffic demand...

Given the locations of mesh routers and their traffic demands, one can have the network configuration designed A network configuration is called a feasible network configuration (F

What is local marketing, What is Local Marketing? Local Marketing: ...

What is Local Marketing? Local Marketing: As marketing programmes are designed to cater the requirements and wants of local customer groups (as trading areas, individual

Fruit store, write an algorithm to calculate fruit for a fruit store for ex...

write an algorithm to calculate fruit for a fruit store for example apple = $1.00 and orange $2.00

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

Case study, Should video game companies continue to alter their products to...

Should video game companies continue to alter their products to include other functions, such as email?

Selling concept and marketing oriented concept, Question: (a) Give five...

Question: (a) Give five differences between the selling concept and marketing oriented concept. (b) Define the roles of advertising, sales promotion, personal selling and pu

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