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

Case study solution, why mayo clinic i so good at customer service

why mayo clinic i so good at customer service

Factor affecting choice of channel of the distribution, Factor affecting ch...

Factor affecting choice of channel of the distribution: the best channel distribution is one of that works best in n the selected by the company. The channel chosen should achieve

Define channels of distribution according to stanton, Normal 0 ...

Normal 0 false false false EN-IN X-NONE X-NONE

Define the concept of relationship marketing, Question 1: (a) Using an...

Question 1: (a) Using an example from the local context, explain how an organisation can counter negative publicity. (b) Discuss the impact that customer retention has on

Products and services - core marketing concept, Products and Services ...

Products and Services Marketing Offers-Services, Products and Experiences Companies introduce needs by putting forth a value proposition, a set of benefits that the

Explain the key function of marketing communication, Explain the key functi...

Explain the key function of marketing communication Many organisations have evolved without marketing being recognised as a key function, let alone as a core philosophy. There

Explain diffrent types of advertisement copy, Q. Explain diffrent types of ...

Q. Explain diffrent types of advertisement copy? Types of advertisement copy: - Advertisement Copy perhaps of various types based on Appeal, functions, Purpose and Media of a

Miss, What is Blackberrys situational analysis and market position

What is Blackberrys situational analysis and market position

What are affective measures of customer satisfaction, What are affective me...

What are affective measures of customer satisfaction? Affective Measures of Customer Satisfaction Measurement: A consumer’s attitude as liking or disliking towards a produ

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