Conditional probability, math, Marketing Management

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 

Posted Date: 2/14/2012 1:39:25 PM | Location : United States







Related Discussions:- Conditional probability, math, Assignment Help, Ask Question on Conditional probability, math, Get Answer, Expert's Help, Conditional probability, math Discussions

Write discussion on Conditional probability, math
Your posts are moderated
Related Questions
What is consumes behaviour? Consumes Behaviour: The most significant issue for the marketers is to classify the requirements of the consumers since customer and consumer m

QUESTION (a) What should management do at the time of Maturity stage to avoid decline of a product? Explain your answer with the help of different approaches at this stage. Sug

buying motives of industrial customer

What are the Advantages of Public Relations? Advantages of Public Relations are as illustrated below: a) This helps in building and having relations along with local comm

What is the meaning of societal marketing concept? Meaning: Societal marketing concept is the idea which the organization must find out the needs, interests and wants of

(a) Find the main external forces triggering the need for organizational change. Pick three and discuss how they might necessitate behavioral change on the part of organization's e

approaches of fmcg companies in test marketing

Give the example of marketing communications For instance, many organisations in airline industry have shifted their attention to the needs of travel trade, customers and compe

Uses of sales promotions: 1.       For facilitating introduction of new products, 2.       For retrieving lost accounts, 3.       For overcoming a unique competitive situ

This assignment requires you to choose: a product and find a market to promote your product, or a market and analyse its needs and find a product to satisfy the