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

Business environment, assess the impact of fiscal and monetary policy on bu...

assess the impact of fiscal and monetary policy on business organisation and their activities ?

What is concept testing strategy development, What is Concept Testing Strat...

What is Concept Testing Strategy Development? Concept Testing: To estimate ideas properly. This may be essential to test product concepts testing is a phase in that a sma

Explain the packet marking approach, Problem (a) Why it is difficult to...

Problem (a) Why it is difficult to perform IP trace-back. (b) (i) Explain the packet marking approach to IP trace-back. (ii) What is the basic problem with this approach

Detail the process of marketing a product, Question 1 Detail the process o...

Question 1 Detail the process of marketing a product Question 2 Write a long note on the budgets of company advertising Question 3 Write a long note on advertising as in

Briefly describe the functionalities of crm sub modules, Question 1: Br...

Question 1: Briefly describe the functionalities of CRM sub modules. List out the benefits of CRM Systems. Functionalities List the benefits  Question 2:

Define the final stage of decision making process, Define the final stage o...

Define the final stage of decision making process. Post Purchase Performance Evaluation: In the last stage of buying process, the product’s performance is estimated. The

Competitiveadvantages, importance of Balancing Customer and Competitor Orie...

importance of Balancing Customer and Competitor Orientations

What is classical conditioning, Question: Classical conditioning theori...

Question: Classical conditioning theories regard organisms as relatively passive entities that can be taught certain behaviors through repetition. (a) What is "classical co

Affected factors of strategies human resource investment, How many factors ...

How many factors are affected of strategies human resource investment decision? There are numerous factors which considered of strategies human resource investment decision. Su

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