The Little Purple Probability Book provides a complement to The Little Green Math Book,which addresses tricky but basic math involving arithmetic and algebra. Probability is a subject that warrants special attention and this short book serves as a stand-alone workshop.
Like most subject matters, probability can be boiled down to a few key concepts. Here is a summary four key concepts as they relate to basic probability and that are showcased in the author’s notes on pages 28–29 of the paperback edition.
Note: There are two sets of terms that are key to understanding how to distinguish among basic probability problems. The first set of terms is “mutually exclusive” and “not mutually exclusive.” The second set of terms is “independent” and “not independent (dependent).” Mutually exclusive means that two events or outcomes do not overlap with one another or cannot occur at the same time. Not mutually exclusive means that two events or outcomes do overlap with one another or can occur at the same time. Independentmeans that two events or outcomes do not influence one another and occur randomly relative to each other. Not independent (or dependent) means that two events or outcomes influence one another and that the occurrence of one event has an affect on the occurrence of another event.
Here are some simple real-life examples to illuminate these terms. Say we are putting on a business conference and inviting attendees as well as guest speakers. The assignment of VIP seating and non-VIP seating is a mutually exclusive outcome. Either a person is in the VIP seats or he or she is not. The same holds true for determining who is an in-state versus out-of-state attendee. An attendee is either in-state or out-of-state with no overlap possible. However, in classifying attendees by profession, we might have overlap between who is a manager and who is an engineer and who is a salesperson and who is an entrepreneur. Obviously, some attendees might fall into more than one category. These categories would, therefore, not be mutually exclusive.
Two tasks might be independent and have no influence on one another. For example, in preparing for the conference, it wouldn’t make any difference whether we made name tags first and then made copies of the conference handouts or made copies of the conference handouts and then made name tags. These events represent separate tasks that have no bearing on one another. On the other hand, two tasks may not be independent of one another; they may, in fact, be dependent on one another. This is true of events that must occur in a certain sequence. In preparing for the conference, we must plan the conference first before inviting speakers to speak at the conference. Likewise, attendees must be registered for the conference, before they can be admitted to the conference and before they ever fill out conference evaluation forms, which are handed out at the end of the conference. In other words, the filling out of a conference evaluation form is dependent upon a person actually attending the conference, which, in turn, is dependent upon a person having first registered for the conference.