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 the scope of marketing information system, What is the scope of Mar...

What is the scope of Marketing Information System? Scope of MIS: Marketing Information system comprises a set of procedures and ways for the continuous analysis and prese

Essentials of headlines for advertisement, Q. Essentials of Headlines for a...

Q. Essentials of Headlines for advertisement? Essentials of Headlines:- It must be attractive. It must be brief. It must be easy to memorise. It must narra

Product margin, The product margin is calculated as product sales minus the...

The product margin is calculated as product sales minus the direct costs of selling the product.

International Marketing Management, Discuss the factors that need to be con...

Discuss the factors that need to be considered when developing an international marketing communication campaign

Communication plan, i need a plan for pop up shops in airports and hotels f...

i need a plan for pop up shops in airports and hotels for cosmetic products, also budgeting for 2 years

Determine the required sales volume, The cost data of Rooney plc is as foll...

The cost data of Rooney plc is as follows: -  Variable cost : Rs 1,800.  Selling Price : Rs 3,500.  Fixed Selling and Distribution cost : Rs 1,700,000 per annum

What is advertising, Q. What is advertising ? Consumer is the heart in ...

Q. What is advertising ? Consumer is the heart in every business. These days attracting and satisfying customers is more difficult than producing the goods. For several product

Need Solution, You can get solutions of you marketing management homework o...

You can get solutions of you marketing management homework on www.onlinesolutionproviders.com

Determination of interest rates, Question 1: (a) ‘The function of the...

Question 1: (a) ‘The function of the financial system is only to channel funds from the surplus units to the deficit units'. Discuss. (b) How far can the liquidity pref

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