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

Value proposition, Value proposition of Cadbury dairy milk?

Value proposition of Cadbury dairy milk?

Position errors, what are the marketion position errors in sri lanka

what are the marketion position errors in sri lanka

Introduction to pricing decision, Introduction to pricing decision: ...

Introduction to pricing decision: Pricing is a very critical decision in the marketing management. The main objective of the firm, that is, to earn a profit very much depend

Case let, how should shoppers'''' Stop develop its demand forecast?

how should shoppers'''' Stop develop its demand forecast?

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

Concepts, what are the core concepts of marketing

what are the core concepts of marketing

small - scale industry products, What pricing strategy would you suggest t...

What pricing strategy would you suggest to a small - Scale Industry Products

Importance of the marketing in the development of economy, Importance of th...

Importance of the marketing in the development of the economy : In all developed countries of the world, marketing is considered to be the key of the economic activities for the

What are the complexity of the communications, What are the complexity of t...

What are the complexity of the communications Exchanges which organisations enter into require the formation of relationships, though tenuous or strong. Andersson (1992) looks

International Marketing, Define International Marketing and furnish its fe...

Define International Marketing and furnish its features

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