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

Maslows hierarchy, An evaluation of Maslow's needs hierarchy Has been...

An evaluation of Maslow's needs hierarchy Has been widely accepted in social science disciplines Criticisms are that the concepts are too general and it can't be tested em

Characteristics of product oriented concept of marketing, Characteristics o...

Characteristics of old or product oriented concept of the marketing: Main characteristics of this concept of marketing are as follows: 1.      It stresses upon the produc

Examples of unfair trade practices, Q. Examples of Unfair Trade Practices? ...

Q. Examples of Unfair Trade Practices? (i) Advertisement concerning weight-loss-claims of any medicine without proper test.  (ii) Using the words 'Government Supported', 'Go

Co branding, what type of co branding is Nike and Apple involved into?

what type of co branding is Nike and Apple involved into?

Explain the rice model, Question : (a) What is a knowledge management ...

Question : (a) What is a knowledge management strategy and what are the basic questions that one needs to ask before developing such a strategy? (b) Using the RICE model,

What are psychological factors of consumer behaviour, What are the psycholo...

What are the psychological factors to determine the consumer behaviour? Psychological: A person’s acquired requirements are influenced by certain psychological factors as lik

What is the meaning of marketing concept, What is the meaning of marketing ...

What is the meaning of marketing concept? Meaning: Marketing concept means that the achievement of organizational goals based on determining the wants and needs of the tar

Explain concept of product line and product mix, Question : (a) Describ...

Question : (a) Describe with examples the concept of product line and product mix. (b) Compare and contrast Reverse Positioning and Breakaway Positioning strategies. (c)

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