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

Introduction to channels of distribution, Channels of distribution Mea...

Channels of distribution Meaning and definition: a major focus of channels of distribution is delivery. It is only through distribution that public and private goods and serv

Examine the importance of using image attributes, The Mauritius Tourism Pro...

The Mauritius Tourism Promotion Authority (MTPA) has undertaken advertising in UK to support low season activity using creative ads that carries the headline So Many Reasons? in or

Break-even analysis, Break-Even Analysis   Break-even pricing (target p...

Break-Even Analysis   Break-even pricing (target profit pricing) is  tactic to setting up price to break- even on the cost of producing and marketing products or to make the ta

Jum jack flash, Do you think Jack is equipped with the managerial skills ne...

Do you think Jack is equipped with the managerial skills needed to head up a team that develops strategies for adapting existing company products into new products for sales in d

What is competitive parity method, Q. What is Competitive Parity Method? ...

Q. What is Competitive Parity Method? Competitive Parity Method: - It is usual approach in which advertising budget is framed in such a manner that our company is at par with

Commercialization or crash introduction strategy development, What is Comme...

What is Commercialization or Crash Introduction Strategy Development? Commercialization or Crash Introduction: A crash introduction is about full scale commercialization

Product packaging, Product packaging: Meaning & definition: The p...

Product packaging: Meaning & definition: The packaging of a consumer product is an important part of the marketing plan. There are many factors to be considered while des

What is total customer satisfaction, Question 1: (a) Explain the import...

Question 1: (a) Explain the importance of the theories of motivation in helping marketing practitioners understand why people buy? (b) (b) Is Customer loyalty synonymo

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