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Definition

TABIn this proposal, I will discuss why the Wikipedia definition for “Probability,” is not a good, valid definition, and needs to be changed. Probability is something that is used every day. It is what helps us further understand the outcomes of the events in life that are uncertain. However, in order to further our knowledge of probability, we must truly understand the definition of the word first. According to Wikipedia, there is not a clear, valid definition for probability, and I propose to change this.

User:Nparibello-NJITWILL/Summer 2012 | Probability

TABThe given Wikipedia definition is as follows: Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth is not certain.[1] 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.[2] 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.

The opening sentence brings great concern as to what probability really is. It begins with, “Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth is not certain.” The word ordinarily is not only ambiguous, but makes the opening sentence tell us very little about what we are reading about. Aside from the ambiguity, the rest of the sentence is extremely confusing as well. Although I am someone who has studied probability not only for my college degree, but also on my own to further my knowledge, I still had to read that sentence over and over again to understand what the writer meant. I would not consider probability an attitude of mind, because this simply does not make sense. The “proposition of interest” and “attitude of mind” are unnecessary and confusing when defining probability. Probability is the analysis of the outcome of an uncertain event. 
TABThe given Wikipedia definition gives several examples of what probability is, rather than defining it. It states that, “The proposition of interest is usually of the form…” This is not only an example instead of a definition, but it is an extremely poor example. The word usually is very vague, leading the reader to believe that the given example does not apply to probability all of the time. The definition also ends with probability in an applied sense. But what does that really mean? Because there are no other examples of another sense that probability applies to, this makes the definition unclear.
TABThe definition then goes on the describe probability in mathematical terms using the range between 0 and 1. For anyone who has not dealt with probability in a mathematical sense, this definition most likely makes little sense. The way it is written is very vague, but what it is trying to say is that there is a range of outcomes in probability starting from 0 (the event will definitely not occur), to 1 (the event will definitely occur). These ranges are also often written in percent form, 0% to 100%. I believe that by adding the fact that these numbers are percentages, the numbers already start to make a more sense and become more valid. The range between these numbers is the percent of likeliness of an outcome. While this definition gave many examples that do not help the reader to further understand probability, I would perhaps include one common example when dealing with the mathematical sense, even though definitions should not include examples. For example, the probability of a fair coin landing heads after it is tossed is .5, or 50%. This is because there are two possible outcomes, heads or tails, and both are equally likely. If the coin had been unfair with heads on both sides, the probability of landing heads would be 1, or 100%, since there are no other possible outcomes. As stated in the original definition, “The higher the probability of an event, the more certain we are that the event will occur.”

TABTwo good quality sources comes from Richard L. Sheaffer in his book, Introduction to Probability and Its Applications, and Glenn Shaffer in his book Probability and Finance. Both Sheaffer and Shaffer are well known mathematicians whose textbooks are used in a vast majority of colleges, including NJIT. Both of their main mathematical focuses aim a probability, making them two of the best sources for this proposal. From a mathematical standpoint, Richard Sheaffer states that “Probability is a numerically valued function that assigns a number P(A) to every event A so that the following axioms hold: P(A) >= 0, and P(S) = 1.” Glenn Shaffer explains these axioms in a more wordy, les