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

Selection of an ads agency by quality and calibre of staff, Q. Selection of...

Q. Selection of an ads agency by Quality and Calibre of Staff? Quality and Calibre of Staff: - Ad-agency has a variety of specialists like models, copy-writers, artists, etc.

Define physical evidence, In marketing the concept of 'physical evidence' r...

In marketing the concept of 'physical evidence' refers to some form of reassurance of service quality before purchase.

#title.ms., factors affecting the product life cycle

factors affecting the product life cycle

Pricing strategy:, Should pricing reflect the cost of making the product, b...

Should pricing reflect the cost of making the product, by an economic value approach, or should prices reflect the perceived value of the product

Product assignment, You are actually a product. Like all products, "you" mu...

You are actually a product. Like all products, "you" must be marketed for success. Write your own mission statement about your career and a goal statement of where you see yourselv

Marketing communication, Problem 1 (a) The development of inter-organi...

Problem 1 (a) The development of inter-organizational relationships is best known through personal selling rather than through exhibitions and trade shows. Explain. Proble

Show the economics benefits of outdoor recreation, Question 1: The exte...

Question 1: The extensive use of outdoor recreational attractions based in natural areas has resulted into increased negative environmental and social impacts. Using local e

What is the meaning of product development, What is the meaning of product ...

What is the meaning of product concept? Meaning: Product concept means that consumers will favor products which offer the most performance, quality and features and which

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