Assignment on Importance of Probability in Business Administration

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.