Page 23 - Probability Demystified

12 CHAPTER 1 Basic Concepts

frequency of E
PðEÞ¼
sum of the frequencies

Empirical probability is sometimes called relative frequency probability.

EXAMPLE: Using the frequency distribution shown previously, find the
probability of selecting a junior student at random.

SOLUTION:
6
Since there are 6 juniors and a total of 25 students, P( junior) ¼ .
25

Another aspect of empirical probability is that if a large number of
subjects (called a sample) is selected from a particular group (called a
population), and the probability of a specific attribute is computed, then when
another subject is selected, we can say that the probability that this subject
has the same attribute is the same as the original probability computed for
the group. For example, a Gallup Poll of 1004 adults surveyed found that
17% of the subjects stated that they considered Abraham Lincoln to be the
greatest President of the United States. Now if a subject is selected, the
probability that he or she will say that Abraham Lincoln was the greatest
president is also 17%.
Several things should be explained here. First of all, the 1004 people
constituted a sample selected from a larger group called the population.
Second, the exact probability for the population can never be known unless
every single member of the group is surveyed. This does not happen in these
kinds of surveys since the population is usually very large. Hence, the 17% is
only an estimate of the probability. However, if the sample is representative
of the population, the estimate will usually be fairly close to the exact
probability. Statisticians have a way of computing the accuracy (called the
margin of error) for these situations. For the present, we shall just
concentrate on the probability.
Also, by a representative sample, we mean the subjects of the sample have
similar characteristics as those in the population. There are statistical
methods to help the statisticians obtain a representative sample. These
methods are called sampling methods and can be found in many statistics
books.
EXAMPLE: The same study found 7% considered George Washington to be
the greatest President. If a person is selected at random, find the probability
that he or she considers George Washington to be the greatest President.