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

Describe the formulation of sales organization, Problem 1: Describe the...

Problem 1: Describe the formulation of Sales organization. Explanation of sales Organisation Step 1 - Sales Strategy Step 2 - Marketing Strategy Step 3 - Sale

Product specialization, Product specialization: Here the firm special...

Product specialization: Here the firm specializes in making a certain product that it sells to several segments. An example would be a microscope manufacturer that sells micr

Advantages of packaging, Advantages of packaging: advantages of the packag...

Advantages of packaging: advantages of the packaging may be divided into three parts: Advantage to manufactures: advantages of the packaging available to manufactures are as

Organizing sales promotion compagins, Organizing sales promotion compagins ...

Organizing sales promotion compagins 1.       Identifying the requirement: the first requirement is to identify the specific requirement of the firm in resg orting to sales p

Needs of marketing and customers, What are the needs of marketing and custo...

What are the needs of marketing and customers? Marketing surrounded through customer needs: Marketing starts along with the customer requirements and needs. Such are turned with

Identify and illustrate five trends for travel demand, Question: (i) ...

Question: (i) Identify and illustrate five trends for travel demand. (ii) Show how these trends would have an impact on the supply of air travel, assuming that there is a

Consumer behaviour, explain VAL"s theory and each types of custmors

explain VAL"s theory and each types of custmors

Exchange, Exchange, transactions, and relationships Marketing occurs w...

Exchange, transactions, and relationships Marketing occurs while people decide to satisfy wants and needs through exchange. Exchange is the act of getting a desired object fro

Explain the term- advertising, Advertising Advertising is a non-person...

Advertising Advertising is a non-personal form of mass communication which offers a high degree of control to those responsible for the design and delivery of advertising mess

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