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Chapter 7: Probability
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Solution:
Let the event of a face that does not display a six be denoted by
A. Thus, the total number of points in
A
will be (50 – 5) = 45. Thus
P
(
A
) =
45/50 = 0.9.
Example 7-10:
During a flu season, a campus health clinic observed that
on one day, 12 out of 60 students examined had strep throats, while a week
later on the same day, 18 out of 75 examined had strep throats. Compute the
relative frequencies for the given information.
Solution:
The relative frequencies are 12/60 = 0.2 and 18/75 = 0.24.
Observe that these relative frequencies are different. However, if data are
collected over a long period of time, the clinic may be able to conclude that
during the flu season, a student who is examined will have strep throat with
a probability of 0.22.
Section Review
7-6 The Law of Large Numbers
In any experiment, the relative frequency for an event will change from trial
to trial. However, if the experiment is conducted for a large number of times
and the running relative frequency is recorded, this accumulated relative
frequency of the event will tend to converge towards a number that is called
the
probability
of the event. This concept is called the
Law of Large
Numbers.
Definition: Law of Large Numbers
When an experiment is conducted a large number of times, the relative
frequency (empirical) probability of an event can be expected to be a close
approximation to the theoretical probability of the event.
This approximation will improve as the number of replications is increased.
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