Page 27 - Probability Demystified

16 CHAPTER 1 Basic Concepts

most of the time, we will not get exactly 50 heads, but we should get close to
50 heads. What will happen if we toss a coin 1000 times? Will we get
exactly 500 heads? Probably not. However, as the number of tosses increases,
the ratio of the number of heads to the total number of tosses will get
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closer to . This phenomenon is known as the law of large numbers. This
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law holds for any type of gambling game such as rolling dice, playing
roulette, etc.

Subjective Probability

A third type of probability is called subjective probability. Subjective
probability is based upon an educated guess, estimate, opinion, or inexact
information. For example, a sports writer may say that there is a 30%
probability that the Pittsburgh Steelers will be in the Super Bowl next year.
Here the sports writer is basing his opinion on subjective information such
as the relative strength of the Steelers, their opponents, their coach, etc.
Subjective probabilities are used in everyday life; however, they are beyond
the scope of this book.

Summary

Probability is the mathematics of chance. There are three types
of probability: classical probability, empirical probability, and subjective
probability. Classical probability uses sample spaces. A sample space is the
set of outcomes of a probability experiment. The range of probability is from
0 to 1. If an event cannot occur, its probability is 0. If an event is certain to
occur, its probability is 1. Classical probability is defined as the number of
ways (outcomes) the event can occur divided by the total number of
outcomes in the sample space.
Empirical probability uses frequency distributions, and it is defined as the
frequency of an event divided by the total number of frequencies.
Subjective probability is made by a person’s knowledge of the situation
and is basically an educated guess as to the chances of an event occurring.