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The probability P(A) of an event A is a measure of the likelihood that the event will occur on any trial. New, but partial, information determines a conditioning event C , which may call for reassessing the likelihood of event A. For a fixed conditioning event C, this new assignment to all events constitutes a new probability measure. In addition, because of the way it is derived from the original, or prior, probability, the conditional probability measure has a number of special properties which are important in applications. Determination of the conditioning event is key.

Introduction

The probability P ( A ) of an event A is a measure of the likelihood that the event will occur on any trial. Sometimes partial information determines thatan event C has occurred. Given this information, it may be necessary to reassign the likelihood for each event A . This leads to the notion of conditional probability. For a fixed conditioning event C , this assignment to all events constitutes a new probability measure which has all the properties of the originalprobability measure. In addition, because of the way it is derived from the original, the conditional probability measure has a number of special propertieswhich are important in applications.

Conditional probability

The original or prior probability measure utilizes all available information to make probability assignments P ( A ) , P ( B ) , etc., subject to the defining conditions (P1), (P2), and (P3) . The probability P ( A ) indicates the likelihood that event A will occur on any trial.

Frequently, new information is received which leads to a reassessment of the likelihood of event A . For example

  • An applicant for a job as a manager of a service department is being interviewed. His résumé shows adequate experience and other qualifications. He conductshimself with ease and is quite articulate in his interview. He is considered a prospect highly likely to succeed. The interview is followed by an extensive backgroundcheck. His credit rating, because of bad debts, is found to be quite low. With this information, the likelihood that he is a satisfactory candidate changes radically.
  • A young woman is seeking to purchase a used car. She finds one that appears to be an excellent buy. It looks “clean,” has reasonable mileage, and is a dependablemodel of a well known make. Before buying, she has a mechanic friend look at it. He finds evidence that the car has been wrecked with possible frame damage that has beenrepaired. The likelihood the car will be satisfactory is thus reduced considerably.
  • A physician is conducting a routine physical examination on a patient in her seventies. She is somewhat overweight. He suspects that she may be prone to heartproblems. Then he discovers that she exercises regularly, eats a low fat, high fiber, variagated diet, and comes from a family in which survival well into their ninetiesis common. On the basis of this new information, he reassesses the likelihood of heart problems.

New, but partial, information determines a conditioning event C , which may call for reassessing the likelihood of event A . For one thing, this means that A occurs iff the event A C occurs. Effectively, this makes C a new basic space. The new unit of probability mass is P ( C ) . How should the new probability assignments be made? One possibility is to make the new assignment to A proportional to the probability P ( A C ) . These considerations and experience with the classical case suggests the following procedure for reassignment. Althoughsuch a reassignment is not logically necessary, subsequent developments give substantial evidence that this is the appropriate procedure.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
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mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
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Samuel
What is Atoms
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Merolyn
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Merolyn
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Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
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Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
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Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
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Achiri Reply
in the mouth
EZEKIEL
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Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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