TOPIC: PROBABILITY & APPLICATION IN BUSINESSPresented To: Mr. Shahzad BabarPresented By: M.HashaamRoll No. : AM552381Class : MBA (B&F) 2nd Semester
ACKNOWLEDGMENTFirst of all thanks of Allah who is most beneficent and the most merciful whose blessings are abundant and favors are unlimited.It is my pleasure to acknowledge the guidance and support of my subject Teacher: Shahzad Babar for their guidance.
AN ABSTRACTProbability theory is an important part of Statistical theory. It is classified in three ways.In business, probability theory is used in the calculation of long- term gains & losses and also for many other business related works.
INTRODUCTION TO PROBABILITY Probability theory is an important part ofstatistical theory that bridges descriptive and inferential statistics. It is the science of uncertainty or chance, or likelihood.A probability value ranges between 0 and 1inclusive and represents the likelihood that a particular event will happen. A probability value of 0 means there is no chance that an will happen and a value of 1 means there is 100 percent chance that the event will happen. Understanding probability is helpful for decision-making.
INTRODUCTION.....(CONT.)Conducting an experiment or sample test provides an outcome that can be used to compute the chance of events occurring in the future. An experiment is the observation of some activity or the act of taking some measurement. Whereas, an outcome is a particular result of an experiment. The collection of one or more outcomes of an experiment is known as an event. For example, a market testing of a sample of new breakfast cereal, new drink, new shoes, new magazine, etc. gives the Director of Production or Director of Marketing a company a preliminary idea (outcome) whether consumers would like the product if it is produced and distributed in bulk.
PROBABILITYClassification of Probability:1) Classical Probability2) Empirical Probability3) Subjective Probability
CLASSICAL PROBABILITY“When there are n equally likely outcomes to an experiment”.The probability of certain events is already known or the resulting probabilities are definitive. For example: (1)The chance that a woman gives birth to a male or female baby (p = 0.50 or ½), (2)The chance that tail or head appears in a toss of coin (p = 0.50 or ½), and (3)The chance that one spot will appear in die-rolling (p = 0.16 or 1/6).
EMPIRICAL PROBABILITY The second one is empirical probability that is based on past experience. The empirical probability, also known as relative frequency, or experimental probability.For example:(1) 383 of 751 business graduates were employed in the past. The probability that a particular graduate will be employed in his or her major area is 383/751 = 0.51 or 51%.(2) The probability that your income tax return will be audited if there are two million mailed to your district office and 2,400 are to be audited is 2,400/2,000,000 = 0.0012 or 0.12%.
SUBJECTIVE PROBABILITY Subjective probability is a probability assigned to an event based on whatever evidence is available. It is an educated guess. Unlike empirical probability, it is not based on past experience. Subjective probability is obtained by evaluating the available options and by assigning the probability. Examples of events that require computing subjective probability:(1) Estimating the probability that a person wins a lottery.(2) Estimating the probability that the GM will lose its first ranking in the car sales.
PROBABILITY DISTRIBUTION Listing of probabilities of all the possible outcomes that could result if the experiment were done.Discrete Probability Distribution: describes a finite set of possible occurrences, for discrete “count data.” For example, the number of successful treatments out of 2 patients is discrete, because the random variable represent the number of success can be only 0, 1, or 2. The probability of all possible occurrences—Pr(0 successes), Pr(1 success), Pr(2 successes)— constitutes the probability distribution for this discrete random variable. There are 2 types for further depth,1. Binomial Distribution2. Poisson Distribution
PROBABILITY DISTRIBUTIONContinuous probability distributions: describe an “unbroken” continuum of possible occurrences. For example, the probability of a given birth weight can be anything from, say, half a pound to more than 12 pounds (or something like that). Thus, the random variable of birth weight is continuous, with an infinite number of possible points between any two values.Normal Distribution: The variable flows without a break and is thus continuous, with no limit to the number of individuals with different measurements. Such measurements are distributed in any of a number of ways. We will consider it, the normal distribution.
APPLICATION IN BUSINESS In business, probability theory is used in the calculation of long-term gains and losses. This is how a company whose business is based on risk calculates "probability of profitability" within acceptable margins. Every decision made in the business world has risk to it. So, in business, you would use probability to take a close look at the companys financial risks. Even the decisions that come down from management all have a probability of success and a probability to fail.
APPLICATION IN BUSINESS Probability in Manufacturing Manufacturing businesses can use probability to determine the cost-benefit ratio or the transfer of a new manufacturing technology process by addressing the likelihood of improved profits. In other instances, manufacturing firms use probability to determine the possibility of financial success of a new product when considering competition from other manufacturers, market demand, market value and manufacturing costs. Other instances of probability in manufacturing include determining the likelihood of producing defective products, and regional need and capacity for certain fields of manufacturing.
APPLICATION IN BUSINESS Scenario AnalysisProbability distributions can be used to create scenario analyses. For example, a business might create three scenarios: worst-case, likely and best-case. The worst-case scenario would contain some value from the lower end of the probability distribution; the likely scenario would contain a value towards the middle of the distribution; and the best-case scenario would contain a value in the upper end of the scenario. Risk EvaluationIn addition to predicting future sales levels, probability distribution can be a useful tool for evaluating risk. Consider, for example, a company considering entering a new business line. If the company needs to generate $500,000 in revenue in order to break even and their probability distribution tells them that there is a 10 percent chance that revenues will be less than $500,000, the company knows roughly what level of risk it is facing if it decides to pursue that new business line.
APPLICATION IN BUSINESS Sales ForecastingOne practical use for probability distributions and scenario analysis in business is to predict future levels of sales. It is essentially impossible to predict the precise value of a future sales level; however, businesses still need to be able to plan for future events. Using a scenario analysis based on a probability distribution can help a company frame its possible future values in terms of a likely sales level and a worst-case and best-case scenario. By doing so, the company can base its business plans on the likely scenario but still be aware of the alternative possibilities.