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

Determine the level of service quality, Competitive tourism and hospitalit...

Competitive tourism and hospitality organisations strive to deliver a high level of service quality to their customers. As a Marketing Manager of one of these organisations, yo

Determination process of a product, Determination process: Estimating ...

Determination process: Estimating the demand for the product: the first step in determining the price of a new product is to estimate the anticipated demand of the product. H

Test marketing, various approaches that are followed by FMCG companies test...

various approaches that are followed by FMCG companies test marketing in marketing management

State the term product according to jerome mccarthy, State the term product...

State the term product according to Jerome McCarthy "A product is more than just a physical product with its associated functional and aesthetic features. It comprises accessor

How customers become brand loyal, Question 1: Brand loyalty is the cust...

Question 1: Brand loyalty is the customer's conscious or unconscious decision, through intention or behaviour, to repurchase a brand continually. In today's highly competitive

What is brand, Brand A brand is a term, symbol, name, or design that i...

Brand A brand is a term, symbol, name, or design that is planned to clearly identify and differentiate a seller's product from the harvest of his or her competitors.

Quantities methods for preparing advertisement budget, Q. Quantities Method...

Q. Quantities Methods for preparing advertisement budget? Statistical techniques similar to multiple profitability, regressions, and simulation or programming techniques and so

Jbhj, consumer profile of typical buyer of rayban

consumer profile of typical buyer of rayban

Kinds of the packaging, Kinds of the packaging: 1.       Consumer pa...

Kinds of the packaging: 1.       Consumer package: it is a kind of the package which holds the required volume of product for the household consumption. For example, tooth

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