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

Algebra 2, the cost of renting a canoe is $20 dollars for the first 4 hours...

the cost of renting a canoe is $20 dollars for the first 4 hours and $3 per hour for additional hours. Sketch a graph of the cost of renting a canoe from 0 to 8 hours. Then write a

State the objectives of marketing communications, State the Objectives of m...

State the Objectives of marketing communications Objectives of this module are to:   Examine concept of exchange in the marketing context;   Assess role of promotion in t

Developing an advertising campaign for the restaurant, QUESTION 1 You h...

QUESTION 1 You have been appointed as a marketing manager for a restaurant selling ‘healthy food' in the city centre. They have asked for your advice on advertising their produ

Factors affecting environmental appraisal, Factors affecting environmental ...

Factors affecting environmental appraisal: given, the same environmental conditions, no two strategies or two organizations would appraise the environment in a similar function. T

Why does your subjects not have consumer behaviour, i need a literature rev...

i need a literature review written by you on a consumer behaviour . Please help I cannot send any email it says error

Explain major environmental issues, Problem 1 Given the importance of e...

Problem 1 Given the importance of environmental issues from a political, social, economic and business point of view, it should come as no surprise that accounting for the env

Market segmentation, Looking for an expert to help with market segmenation ...

Looking for an expert to help with market segmenation process

Basic model of consumer decision making, (a) Differentiate the substitutio...

(a) Differentiate the substitution effect and income effect of a price change and illustrate same by way of a diagram for the case of a normal good. (b) Describe with example t

Marketing, identify and briefly describe four treands in the macro/market

identify and briefly describe four treands in the macro/market

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