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
Consumer Buying Behaviour Markets (and those which they serve) must be understood before marketing strategies may be developed. The consumer market purchase services and goods

How should Shoppers? Stop develop its demand forecasts?

Define the Advertisement contents? Advertisement contents Message : - Consist of opinion, symbols, Facts and Pictures related to the product. Purpose: -        Communi

Mauritius is an open economy. The recent global financial crisis, world climatic changes impacting on food prices, and the strong demand from the BRIC(Brazil, Russia, India, and Ch

Q. Choice of an advertising agency by location? A main consideration in the choice of an advertising agency is location of office of agency. A significant amount of communicati

Characteristics of the promotional types: Factor Advertising Publicity Personal selling Sales promotion Audien

income inreased by 10% later decreased by 10%. total change in % in income

what are advantages and disadvantages of five maketing philosophies

what gaps between core marketing aspects have kellogg''s successfully managed to bridge?

Q. Message - Source of advertisement? Message-Source:- Person who converse the message of advertiser to the target audience. Also known as brand-ambassador instance sport