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
Q. How to select a Media for advertisement? Media Reach and Coverage: Such media must be selected which has wide reach and can cover our target customers. If the advertiser h

what management skills did jack demonstrate as a marketing manager at the travel products company? What management skills did he demonstrate as a VP at the consumers product firm?


i submitted an assignment. that assignment is accessible to your site . i confirmed it beforehand. but some mishappening is there. its not in record perhaps that i got an assignmen

define marketing .its importance

approaches that are followed by FMCG companies

Name FIVE factors that can influence an individual when deciding whether or not to purchase a product. The degree to which the product satisfies a need or a want. The social

QUESTION Environment is a factor in the development of planned communication. Competitors can think of changing the way of presenting their services and products and ultimatel

Advertiser must avoid giving his advertising work that agency that handles the advertising work of his competitor. For the reason that in that case ad agency mayn't be in a positio

what are the problems with green marketing? And what are there remedies?