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

Marketing, Does marketing exist solely to increase profit? If this is the c...

Does marketing exist solely to increase profit? If this is the case, then marketing in nonprofit organizations can be said to be useless. discuss

Undifferentiated approach for selecting target market, What is undifferenti...

What is undifferentiated approach for selecting target markets? Undifferentiated Approach: In total market or undifferentiated approach, a company develops a particular

What is influence of the human resource information system, What is influen...

What is influence of the human resource information system? Affect of Human Resource Information System (HRIS): Firms have invested upon the software for P+R as Oracle, S

Calculate the total time, Question: a) Suppose a web client makes a re...

Question: a) Suppose a web client makes a request for a resource located on an internal web server using on a 10Mbps Ethernet LAN. The client and the server are connected via

What kind of market structure is the automotive industry, There are many wa...

There are many ways to explain the market structure of the automotive industry.: One of heterogeneous purchasers makes up the population and nearly homogeneous sellers. This mea

State the term- channels of distribution, State the term- Channels of distr...

State the term- Channels of distribution You are aware that when a manufacturer of a product is located at one place, its consumers are located at innumerable places spread all

Marketing, what are the core marketing concepts?

what are the core marketing concepts?

Should video game companies continue to alter their products, Should video ...

Should video game companies continue to alter their products to include other functions, such as e-mail?

Explain about the use associated segmentation, Explain about the Use Associ...

Explain about the Use Associated Segmentation. Use Associated Segmentation: An extremely effective and popular form of segmentation categories consumers in conditions of

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