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

FOUR TRENDS IN THE MACRO MARKET, Identify and briefly describe four trends ...

Identify and briefly describe four trends in the macro/market environment that will have or recently had an influence on the selected industry.

Explain the role of managers in marketing communication, Explain in role of...

Explain in role of managers in marketing communication Managers are now required not only to find new ways to communicate but also to do so on reduced budgets and they should a

Management Accounting Assignment, Compare and contrast three planning tools...

Compare and contrast three planning tools used in management accounting, indicating how effective you judge each to be and why. Your judgments should be supported by evidence.

Show the nature of customers, Q. Show the Nature of Customers? Nature ...

Q. Show the Nature of Customers? Nature of Customers: An appropriate media plan should consider the type or class of consumers for whom advertising is to be done. Different c

Identify and explain how the product life cycle, Question: In the conte...

Question: In the context of a product from the fashion industry: a. Describe the concept of a product as a tangible and intangible "bundle of benefits? that provide

Write a report on swot analyses for the company, According to the MCCI Busi...

According to the MCCI Business Confidence Indicator (September 2010), the morale of business leaders is morose with a drop to 96.3 of the confidence level index(March 2010=100)

Segmentation, Identify and briefly describe the criteria you would use to h...

Identify and briefly describe the criteria you would use to help establish whether a variable is useful as a segmentation base.

Explain about the individual customer marketing, Explain about the Individu...

Explain about the Individual Customer Marketing. Individual Customer Marketing: As a marketers detects as several segments as there are consumers then each segment is com

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