Probability is ordinarily used to
describe an attitude of mind towards some proposition of whose truth is not
certain. The proposition of interest is
usually of the form "Will a specific event occur?" The attitude of mind is
of the form "How certain are we that the event will occur?" The
certainty we adopt can be described in terms of a numerical measure and this
number, between 0 and 1, we call probability.

The higher the probability of an event, the
more certain we are that the event will occur. Thus, probability in an applied
sense is a measure of the confidence a person has that a (random) event
will occur. Probability has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial
intelligence/machine learning and philosophy to, for example, draw inferences
about the expected frequency of events. Probability theory is also used to
describe the underlying mechanics and regularities of complex systems.**What is Probability :**

We use phrases like "the
probability of this coin coming up heads is 1/2", and "the odds on
Manchester United winning their match are 2 to 1", and "the chance of
dying of cancer is 30%". But what do these numbers actually mean? There
are fundamentally different views about this, which can lead to very different
ideas about how to deal with uncertainty.

The mathematics of probability may be
sorted out, but the underlying concepts are not straightforward. Maybe that's
why the study of probability only started 350 years ago, which is relatively
recent compared to other mathematical ideas.

The
two faces of probability introduces a central ambiguity which has been around for 350 years and
still leads to disagreements about when probabilities can be used. For example,
iIf I throw a die, look at the result but don't show it to you, what is the
probability (for you) that it is a 6? In one interpretation it is still 1/6,
since you don't know the result, but in another interpretation the probability
is either 1 or 0, since the die shows either a 6, or it doesn't.

**Importance of Probability in Business Administration**

Probability has a popular meaning
that is not the same as the mathematical meaning. As a small-business owner,
you may act on hunches, guesses and instincts. After such actions, you might
even say you thought a certain outcome was "probable." However, the
mathematics of probability has rules that you can use in a much more
disciplined way than guesswork to predict possible outcomes for your business
plans.

**Classical Approach**

The classical approach to using
probability depends on several future events that are equally likely to happen.
In rolling a die, for example, the odds are equally likely for rolling a 1, 2,
3, 4, 5 or 6. If you roll the die once, you have a 1 in 6 chance of getting the
number you want. The formula is the number of favorable outcomes divided by the
total number of possible outcomes. Note that if you roll the die twice, the
odds are 2 in 12 that you will get the number you want (this is the same value
as 1/6). This is because the possible outcomes double if you throw the die
twice.

**Using the Classical Approach in Business Administration**

You can use the classical approach
to probability when making business decisions where you don't know the
likelihood of several possible outcomes. You assume they are all equally
likely, then look at how many attempts you will be able to make. However, in
your business, if 6 possible outcomes are equally likely, but they are not
affected by how many times you try, you can cut your odds in half with repeated
effort. For example, if you make 2 tries, your effort will have a 2 in 6
chance. Notice that 2/6 = 1/3. You have moved from a 1 in 6 chance of success
to a 1 in 3 chance.

**Relative Frequency Approach**

The relative frequency approach uses
the past to make predictions about the future. You look at how many times an
event has happened and then look at how many opportunities exist for the event
to occur. The formula is the number of times an event occurred divided by the
total number of opportunities for the event to occur.

**Using Relative Frequency Approach in Business Administration**

You can use relative frequency to
improve your business decisions. For example if your research shows there are
75 failures for every 100 business startups attempted, you would say that 75
out of 100 startups fail. This reduces to 3/4. That would mean 3 out of 4
startups fail. If you don't do something to change your odds, you can expect
that failure probability. This mathematical reality can give you a sense of
urgency in your efforts to be the 1 out of 4 that succeeds. In fact, you could
study the successes to see how they changed the odds in their favor.

**Benefits of Probability**

One of the things i have learned from poker is that
probability is not an indicator of what's to happen in the future, however, by
playing the odds on a continuous basis you are assured to come out on top. just
make sure to take the good odds, a 51/49 split is not a good chance in the
world of probability. Anything over 70% (i believe) is considered to be a good
risk vs. reward assessment.

**The Importance of Probability Sampling**

Sampling should be designed to guard against
unplanned selectiveness. A replicable or repeatable sampling plan should be
developed to randomly choose a sample capable of meeting the survey's goals. A
survey's intent is not to describe the particular individuals who, by chance,
are part of the sample, but rather to obtain a composite profile of the population
of interest. In a bona fide survey, the sample is not selected haphazardly or
only from persons who volunteer to participate. It is scientifically chosen so
that each person in the population will have a measurable chance of selection –
a known probability of selection. This way, the results can be reliably
projected from the sample to the larger population with known levels of
certainty/precision, i.e. standard errors and confidence intervals for survey
estimates can be constructed. Critical elements in an exemplary survey are: (a)
to ensure that the right population is indeed being sampled (to address the
questions of interest); and (b) to locate (or "cover") all members of
the population being studied so they have a chance to be sampled. The quality
of the list of such members (the "sampling frame") whether it is
up-to-date and complete is probably the dominant feature for ensuring adequate
coverage of the desired population to be surveyed. Where a particular sample
frame is suspected to provide incomplete or inadequate coverage of the population
of interest, multiple frames should be used.

**Conclusion :**

Importance of Probability in Business Administration has been given an axiomatic mathematical
derivation in probability theory, which is used widely in
such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for
example, draw inferences about the expected frequency of events. Probability
theory is also used to describe the underlying mechanics and regularities of complex systems.