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

Global markets, Understanding other cultures is vital to success in the glo...

Understanding other cultures is vital to success in the global marketplace. Refer to Table 21-3 which lists some blunders in International Marketing. One of my favorite blunders ha

Describe how branding can benefit a tourism, Question 1: a) Explain dif...

Question 1: a) Explain different types of pricing techniques. As a consumer which method do you personally prefer to deal with? Justify your answer. b) Describe how brandi

Market crystallization, A market development stage is the one that refers ...

A market development stage is the one that refers to the attempt needed to recognize a latent market (i.e., organizations that share a like need or want for something that does no

Define marketing mix according to philip kotler, Define marketing mix accor...

Define marketing mix according to Philip Kotler According to Philip Kotler "Marketing Mix is set of controllable variables that firm can use to influence buyer's response".  C

Explain about packaging in marketing function, Explain about packaging in m...

Explain about packaging in marketing functions of physical treatment. Packaging: Packaging has become one of the necessary services of modern marketing. This acts like a m

Prepare a presentation on new products, Question 1 (a) Relate the impor...

Question 1 (a) Relate the importance of well linking any visual aid to its specific message and explain the functions that visual aids can have. (b) The marketing officer of

Henry assael model of buying decision behaviour along with t, henry assael ...

henry assael model of buying decision behaviour along with the diagram

Draw a demand curve, Suppose D1 represents the demand curve for paperback n...

Suppose D1 represents the demand curve for paperback novels, D2 represents the demand curve for gasoline, S1 represents the supply curve for paperback novels and S2 represents the

Forward integration, A planning in which a business expands its activities ...

A planning in which a business expands its activities to include allocation or lines of business related to the selling of its core products.

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