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 is customer response to a new product in research, How is customer resp...

How is customer response to a new product identified in marketing research? Identify customer response to a new product: This is also known as product testing. Marketing

Current balance sheet, Well Water has been in business nearly 100 years, ha...

Well Water has been in business nearly 100 years, has always been owned by the Gerry family, and is the second largest bottled water firm in the area in terms of annual sales. To h

Role of the environment scanning in the organizations, Role of the environm...

Role of the environment scanning in the organizations: property used environmental scanning can help to ensure organizational success. The specific organizational roles or functio

Differences between goods and services, Question: ‘The basic difference...

Question: ‘The basic differences between goods and services offer the biggest challenges to Service marketers'. With reference to services you are familiar with, discuss th

Purchase and decision implementation in decision making, Explain about purc...

Explain about purchase and decision implementation in decision making process. Purchase and Decision Implementation: When the decision to buy has been made, the way of pu

New/morden concept of the marketing, New/Morden concept or product oriented...

New/Morden concept or product oriented concept of the marketing : Modern concept of marketing is a customer oriented concept. This concept is based on the assumption that a busi

What is skimming pricing strategy, What is Skimming Pricing Strategy? ...

What is Skimming Pricing Strategy? Skimming Pricing Strategy: This strategy comprises selling the new product at higher price and therefore limiting oneself to the upper

Idea generation - new product development process, New Product development ...

New Product development Process Idea Generation In the new-product development procedure, the first step is idea generation, which is the systematic discovery for new p

.., why we need to study promotion in marketing?

why we need to study promotion in marketing?

International marketing., Companies entering emerging markets for the first...

Companies entering emerging markets for the first time must exercise particular care in choosing a channel intermediary. Usually a local distributor is required. What are some of t

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