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

What are the stages of product life cycle, What are the stages of product l...

What are the stages of product life cycle? Stages of Product Life Cycle: introductory stage, growth stage, maturity stage and decline. Products have restricted life. A pro

Define the final stage of decision making process, Define the final stage o...

Define the final stage of decision making process. Post Purchase Performance Evaluation: In the last stage of buying process, the product’s performance is estimated. The

What is meant by marketing research, Question: (a) What is meant by ma...

Question: (a) What is meant by marketing research? What are the main sources of data which should be included in a research brief? (b) What is consumer black box? How many

Case study, Case Study - Horlicks Horlicks is the name of a company and ...

Case Study - Horlicks Horlicks is the name of a company and of a malted milk hot drink. This brand is the leading product in the hot milky drinks market and has been associated

Explain numbers of features in marketing offer customers, Explain about the...

Explain about the numbers of features in marketing offer more customers. While the number of features into a marketing offer is more the customer feels which the marketer has o

Frederick herzberg''s dual factor, Explain the relationship between Frederi...

Explain the relationship between Frederick Herzberg's dual (two) factor motivation theory and job enrichment. Hygiene factors contain pay, status, working conditions, rules and

Relationship marketing, Relationship Marketing This approach is used to...

Relationship Marketing This approach is used to marketing emphasizes the importance of personal relationship building with all parties among consumers, suppliers and distributo

Marketing mix, This comprises the marketing tools and techniques an organiz...

This comprises the marketing tools and techniques an organization uses to achieve its targets relative to a specific goal market audience.

Marketing as a part of total environment, Illustrates the total environment...

Illustrates the total environment in marketing? Marketing is a part of total environment: Total environment may be explained as the combination of all the resources and In

Factors affecting marketing planning, Factors affecting marketing planning:...

Factors affecting marketing planning: a large number of factors affect the long term marketing planning. These factors can be grouped under four categories: Internal factors:

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