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

What is local marketing, What is Local Marketing? Local Marketing: ...

What is Local Marketing? Local Marketing: As marketing programmes are designed to cater the requirements and wants of local customer groups (as trading areas, individual

Differentiate between inbound and outbound marketing, QUESTION a) Diffe...

QUESTION a) Differentiate between inbound and outbound marketing. b) The following statement was the closing statement from the case: "most businesses- including HubSpot

Outline a marketing research project, Question: a) Wilson Publishing - ...

Question: a) Wilson Publishing - which publishes a series of textbooks in management by different authors - intends to give a new book on Marketing. Marketing is an area they h

Trigogometry, If b+c=3a,then the value of cotB/2 cotC/2 is equal to....

If b+c=3a,then the value of cotB/2 cotC/2 is equal to....

Marketing management philosophies, Marketing management philosophies 1...

Marketing management philosophies 1.      The production concept: The production concept holds that consumers will favour products that are available and highly affordable;

Inerfa ce, What are sabmiller interfaces with loqgistics, marketing, distri...

What are sabmiller interfaces with loqgistics, marketing, distribution

Marketing, in context of marketing, explain three approaches that were use ...

in context of marketing, explain three approaches that were use in early days

Match supply with demand in a profitable manner, Question: By the early 70'...

Question: By the early 70's you realised the market for toys in the US is about to change. What strategies would you recommend for the future (next 10 years) in terms of new produc

Inquiry into unfair trade practices, The inquiry beside unfair trade practi...

The inquiry beside unfair trade practices can be initiated: (i) On receiving a objection from any consumer (ii) On receiving a objection from registered-consumer-association

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