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

Develop a quality management plan, XYZ Limited, finalist for the European Q...

XYZ Limited, finalist for the European Quality Award (EQA), has doubled its share of the quality carpet sector in recent years and now holds over 10 per cent of the world market fo

APPROACHES , VARIOUS APPROACHES THAT ARE FOLLOWED BY FMCG COMPANIES IN TEST...

VARIOUS APPROACHES THAT ARE FOLLOWED BY FMCG COMPANIES IN TEST MARKETING

Segmentation, With aid of an example of a manufacturer, define segmentation...

With aid of an example of a manufacturer, define segmentation?

#titsecondary source, list out the secondary sources of information while p...

list out the secondary sources of information while pursuing market research?

Explain the stage involved in the product life cycle concept, QUESTION 1 ...

QUESTION 1 (a) Explain the stages involved in the Product Life Cycle concept and their relevance in marketing decision making. You may use any product/service as an example to

Difference between business and systems integration, 1. Offer an example, r...

1. Offer an example, real or imaginary, of firms in each of the following three situations (do not use the Wiztech case as the basis of your response). Thoroughly explain your exam

Marketing, #quAssume that a multi-specialty medical group has decided to se...

#quAssume that a multi-specialty medical group has decided to segment the market in the community by income level. The group has decided to target a small niche of middle-aged, whi

What are the ways to decrease the customer defection rate, What are the way...

What are the ways to decrease the customer defection rate? To decrease the customer defection rate, a company should: a) Explain and measure the retention rate. b) Classi

Buying motives, buying motives of industrial customer

buying motives of industrial customer

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