What are the classical, empirical, and subjective approaches to probability, and when is it appropriate to use each approach?

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Probability is a numerical value that describes the chance that something will happen. Probability can be expressed as a decimal, fraction, or whole number. There are three types of probability including: classical, empirical, and subjective. The classical and empirical probabilities are objective approaches. (Lind, Marchal, & Wathen, 2015)

Classical probability is based on the assumption that the outcomes of an experiment are equally likely. The probability of an event is found by dividing the number of favorable outcomes by the number of possible outcomes. It is only appropriate to use classical probability when all events are equally likely. A business example would be that there are seven males and three females that are interviewing to work at your same place of employment. The probability of your boss choosing a female is 3/10 or .3. (Lind, Marchal, & Wathen, 2015)

Empirical probability is based on the number of times an event occurs as a proportion of a known number of trials. Empirical probability is found by deciding the number of times the event occurs by the total number of observations. Empirical probability should be used to determine future events. (Lind, Marchal, & Wathen, 2015) For example, your research indicates that seventy-five out of one hundred small businesses fail within their first year. You can conclude that 75/100 or 3/4 of small business fail within one year. Therefore, you should make smart business decisions so that you do not fail as well. (Writer, 2013)

Subjective probability is when there is little or no experience or information on which to base a probability. There is no mathematical equation to calculate subjective probability. Subjective probability should be used for estimations based on your beliefs or feelings. For example, you can estimate the likelihood that your business will profit 10% more in 2017 than it did in 2016. (Lind, Marchal, & Wathen, 2015)

Lind, D. A., Marchal, W. G., & Wathen, S. A. (2015). Statistical techniques in business & economics. New York, NY: McGraw-Hill Education.

Writer, L. G. (2011, October 13). What Is the Importance of Probability Rules in a Business? Retrieved March 20, 2017, from http://smallbusiness.chron.com/importance-probability-rules-business-31263.html.

What are the classical, empirical, and subjective approaches to probability, and when is it appropriate to use each approach? Give business examples to support the different parts of your answer.

Even though there are different approaches to probability such as the ones listed in the topic question.  I do feel it is important to know what probability is.  The book states that probability is a value between zero and one, inclusive, describing the relative possibility an event will occur (Lind, Marchal, & Wathen, 2015). Some important terms that are associated with probability are experiment, outcome and event.  Experiment is process that leads to the occurrence of one and only one of several possible outcomes while the outcome is a particular result of an experiment.  An event is a collection of one or more outcomes of an experiment. (Lind, Marchal, & Wathen, 2015).

The classical approach to probability based on an assumption that the outcomes of the experiment are equally likely (Lind, Marchal, & Wathen, 2015).  When using this approach, you divide the number of favorable outcomes by the number of possible outcomes.  Business use the classical approach when they do not know the likelihood of certain events.  For example, if a business is making a decision that has X amount of outcomes that are equally likely, even though they are not affected by the number of times you try.  You can cut the number in half with the classical approach (Chrone).  The book gives us the example that this approach is appropriate when used for lotteries and finding out the probability of winning when picking X amount of numbers (Lind, Marchal, & Wathen, 2015).

Empirical probability is the probability of an event happening is the fraction of the time similar events have happened in the past.  Solving this approach requires taking the number of times the event has occurred and dividing it by the total number of observations (Lind, Marchal, & Wathen, 2015). This event is based on what is called the “law of large numbers”.  Empirical probability is closely related to relative frequency.  Therefore, this approach has been used with the capital asset pricing model even though the results turn our slightly mixed (Investopedia).  One of the best examples for empirical probability is tossing a coin in the air.  This approach will help determine the relative frequency of the coin landing on heads or tails (Lind, Marchal, & Wathen, 2015).

The third and final approach is subjective probability.  Subjective probability is the likelihood of a particular event happening that is assigned by an individual based on whatever information is available.  Examples for this approach include outcomes of sporting events, automobile accidents and for cuts or gaines in the U.S. economy (Lind, Marchal, & Wathen, 2015).

References:

Lind, D.A., Marchal, W.G., & Wathen, S.A. (2015). Statistical Techniques in Business and Economics. New York, NY: McGraw-Hill Education.

Staff, I. (2007, May 28). Empirical Probability. Retrieved March 21, 2017, from http://www.investopedia.com/terms/e/empiricalprobability.asp