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

What is advertising, Q. What is advertising ? Consumer is the heart in ...

Q. What is advertising ? Consumer is the heart in every business. These days attracting and satisfying customers is more difficult than producing the goods. For several product

Test marketing, what is test marketing?explain the various approaches that ...

what is test marketing?explain the various approaches that are followed by FMCG companies in test marketing

Explain with example the concept of anatomy of a product, (a) Explain with ...

(a) Explain with example the concept of anatomy of a product. (b) Differentiate between a brand mark and a brand name. (c) Draw an appropriate diagram to illustrate the impor

Accurate processing of data and safeguarding of privacy, Describe, with exa...

Describe, with examples, the TWO forms of IT/IS controls that exist to ensure complete, accurate processing of data and safeguarding of privacy and security. There are two cate

Quality assurance in packaging and manufacturing goods, how to maintain qua...

how to maintain quality assurance in management? whose procedures of manufacturing for goods in Pharmaceutical companies. please discuss in easy words?

Responsibility of devising marketing communications, CASE STUDY-  Chubb Sec...

CASE STUDY-  Chubb Security Systems Chubb, an organization noted for its locks and security systems, developed a security product particularly suited to manufacturing organizat

Various stages in the pricing of menus, Question 1: What is the Food Pr...

Question 1: What is the Food Production Cycle? Explain in detail the process of production, sales and service with regard to supervision, quality and control procedures. Qu

Three uses of line stretching, depict the concept of line stretching and th...

depict the concept of line stretching and the three uses for it?

Feedback from customers for better customer satisfaction, Question 1: (...

Question 1: (a) CRM means different things to different people. For one it is direct mailing for others it is an IT system. Draw a diagram and discuss the basic model for CR

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