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

Oligopoly market, Oligopoly Market The majority of the world’s diamonds com...

Oligopoly Market The majority of the world’s diamonds comes from Country A and Country B. Suppose that the marginal cost of mining a diamond is $1,000 per diamond and that the dema

Show the media-availability in advertising, Q. Show the Media-Availability ...

Q. Show the Media-Availability in advertising? Media-Availability: Sometimes it is probable that desired space for advertisements in print media is already booked by some oth

Global marketing, Global Marketing The activity of a global corporation...

Global Marketing The activity of a global corporation  that searches to get long- run, large-scale production efficiencies by producing standardized products of good value and

Total ordering and holding costs, A manufacturing company has determined fr...

A manufacturing company has determined from an analysis from its accounting and its production data for a certain part that its demand is 9000 units/annum and is uniformly distribu

Illustrate ethical aspects of advertising, Q. Illustrate ethical aspects of...

Q. Illustrate ethical aspects of advertising? 1) Effect on culture: - Culture demotes to the way of life of group of people. It comprises life customs, morals, style, values,

Why ''supply'' has been more significant than ''purchasing'', Explain why '...

Explain why 'Supply' has been described as being more significant than 'Purchasing' for an organisation.  Purchasing Purchasing deals with the day-to-day buying of goods.

Illustrate the term image pricing, Illustrate the term Image Pricing? ...

Illustrate the term Image Pricing? Image Pricing: It is a variant of premium pricing as the objective is the similar to signal quality to uninformed buyers and utilize th

VALS model, I need help on making VALS model of Mobilink JAzz Octane. Plzzz...

I need help on making VALS model of Mobilink JAzz Octane. Plzzz help

Sprite Brand, What are the different strategies in sprite brand

What are the different strategies in sprite brand

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