"Probability and
its Application in Business"
In this session of Business Statistics we
started with the topic Probability. As there are 3 methods:
·
Ratio
chance
·
Percentage
chance
·
Probability
We will be dealing mainly with the probability in our course
The 3 Approaches which we will be using to solve the problems
in our business organizations are:
A priori (Prior
information):
Something which we know through commonsense or that can be derived by deductive
reasoning.
For example: If a company A is trying to get the project from Client X
and there is only 1 business competitor of A that is company B and also if it
is known that in past Client X has already broken relationship with Company B
then there is a high probability that company A will get the project from
Client X.
Empirical (Information
Collected): Objectively
drawn from data available. It gives a point estimate.
For example: If we have to hire employees for aviation industry and 10
candidates have applied for the job and if we know that out of 10, 5 employees
have already prior work experience in some private airways and remaining 5 have
worked in steel industry then based on analysis of profiles of candidates we
can easily hire those 5 employees who have prior relevant work experience in
the aviation industry.
Subjective (Judgment): Subjective probability gives a
range based on number or data which is not fixed and may take different value
in different situation.
For example: Investing in share market or mutual funds is one of the examples
because investment world is filled with people making incorrect subjective
judgments.
3 Event properties:
Mutually Exclusive events:
Two events are 'mutually exclusive' if they cannot occur at the
same time. An example is tossing a coin once, which can result in either heads
or tails, but not both.
For example: Profit and Loss associated with the organization is a
mutually exclusive event. Particular department of an organization face either
profit or loss in the quarter results.
Independent events: In probability theory, two events are independent (alternatively
statistically (alternatively statistically independent, marginally
independent or absolutely independent) means that the occurrence of
one does not affect the probability of the other.
For example : If in a Computer Software firm ,IT department Manager
faces problem due to lack of upgraded computer system available for his team
and at the same time Security Manager of the firm faces problem due to lack of
availability of security guards . Both the problems belong to same Software
firm but still both the problems are independent of each other.
Dependent events: Two events are dependent if the
outcome or occurrence of the first affects the outcome or occurrence of the
second so that the probability is changed.
For example : If an employee of a particular organization is facing some
personal problems in his life due to which he is not able to concentrate on his
work which in turn results in delay in achieving timelines of his work which
indirectly impacts the project of the organization. Hence all the events are
dependent and the outcome or occurrence of the first affects the outcome or
occurrence of the second.
3 laws of probability:
Additional law: A statistical property that states
the probability of one and/or two events occurring at the same time is equal to
the probability of the first event occurring, plus the probability of the
second event occurring, minus the probability that both events occur at the
same time. Mathematically, this property is denoted by:
P(Y u Z)=P(Y) +P(Z)-P(Y n Z)
Conditional law: A conditional probability law is the probability law
in which an event will occur, when another event is known to occur or to have
occurred. If the events are A and B respectively, this is
said to be "the probability of A given B". It is
commonly denoted by P(A|B), or sometimes PB(A). P(A|B) may or
may not be equal to P(A), the probability of A. If they are
equal, A and B are said to be independent. For example, if a coin is flipped
twice, "the outcome of the second flip" is independent of "the
outcome of the first flip".
For example:
Let's consider the following scenario: Cyber Video Games,
Inc., has been running a television ad for its latest game, “Ultimate Hockey.”
As Cyber Video's director of marketing, you would like to assess the ad’s
effectiveness, so you ask your market research team to make a survey of video
game players. The results of their survey of 50,000 videogame players are
summarized in the following chart.
Saw Ad Did Not See Ad
Purchased Game 1,200 2,000
Did Not Purchase Game 3,800 43,000
Conditional Probability in this case = ( Number of people who saw the ad and
purchased the game / Total number of people who saw the ad ) =
1200/5000 = 0.24
Multiplicative law: The Probability of both events occurring can
be calculated by rearranging the terms
in the expression of conditional probability .
P(A and B) = P(A given B) * P(B)
Bayes’ theorem : It gives us
the actual probability of an event given the measured test
probabilities. For example, you can:
§
Correct for
measurement errors. If we know the real probabilities and the chance of a false
positive and false negative, we can correct for measurement errors.
§
Relate the actual
probability to the measured test probability. Bayes’ theorem lets us
relate Pr(A|X), the chance that an event A happened given the indicator X, and
Pr(X|A), the chance the indicator X happened given that event A occurred. Given
mammogram test results and known error rates, we can predict the actual chance
of having cancer.
Venn diagram: Venn diagrams were invented by John Venn as a way of
picturing relationships between different groups of things. "Venn
diagrams" are actually "Euler" diagrams.
Mathematical term for "a group
of things" is "a set", Venn diagrams can be used to illustrate
both set relationships and logical relationships.
When
drawing Venn diagram, there will be two, three or four overlapping circles..gif)
Fig 1: Venn
diagram representing 2,3 and 4 cases respectively
These venn
diagram can be used for calculating probability in real time situation.
Session taken by: Professor Uday Bhate
Blog written by : Nitin Boratwar
Roll no. : 2013179
Group Members
Nidhi
Nitesh Singh Patel
Palak Jain
Pallavi Bizoara
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