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

Concept of rules and discretionary central banking policies, Question 1: ...

Question 1: (a) Clearly explain the concept of rules versus discretionary central banking policies. (b) Discuss the various risks faced by the financial system and disc

Explain the stages of product life cycle, Q. Explain the Stages of Product ...

Q. Explain the Stages of Product life cycle? Stages of Product life cycle. a) Introduction stage - Advertising for consumers and Personal selling for middlemen. b) Growth

Core concepts, what are the core concepts of marketing

what are the core concepts of marketing

Mkt mgt, various approaches of test marketing

various approaches of test marketing

Explain the stage involved in the product life cycle concept, QUESTION 1 ...

QUESTION 1 (a) Explain the stages involved in the Product Life Cycle concept and their relevance in marketing decision making. You may use any product/service as an example to

Explain the thinking of public about the public relations, Explain the thin...

Explain the thinking of public about the public relations. The public often think of public relations like a glamorous job. These relations people seem to have been tarred alon

Give a brief overview about advertising, Give a brief overview about Advert...

Give a brief overview about Advertising. Meaning of Advertising: “Any paid type of non-personal presentation and promotion of concepts, services or goods by an identified

Analyze the economic & demograpic env. of himachal pradesh, study the envi...

study the environmental & economical trends prevailing in Himachal Pradesh & prepare a business plan for launching a new product

Green marketing., what are the problems with green marketing? And what are ...

what are the problems with green marketing? And what are there remedies?

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