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Chapter 7: Probability
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Solution:
The possible points in the sample space are given in the set
S
.
(Just mimic
Example 7-5
).
S
= {
RRR, RRB, RBR, RBB, BRR, BRB, BBR, BBB
}.
Example 7-8
: For
Example 7-7
, what is the probability of a player winning
the game?
Solution:
Recall, a person wins the game if all three chips match each
other. This will occur when all there chips are either red or all three are
blue. Let
A
be the event of winning. Then
A
= {
RRR, BBB
}.
Event
A
is made up of two simple events, and there are 8 simple events in
the sample space. Thus,
P
(
A
) = 2/8 = 0.25.
In the next section, we will discuss the relative frequency or the empirical
approach to probability. This approach is based on the proportion of times
an event is observed over a fixed number of exactly repeatable trials.
Section Review
7-5 Relative Frequency or Empirical Probability
Probability can be measured by relative frequency in which the trials are
exactly repeatable, as in the case of tossing a coin a repeated number of
times or selecting items.
For instance, if we flip a fair coin once, we say that the probability of getting
a head is 1/2 = 0.5. This is because we have two possible outcomes: a head
or a tail with the sample space S = {
H
,
T
}. This probability of 0.5 is the
theoretical (classical) probability of observing a head on a single toss of a
coin. In an experiment, however, if we flip the coin 10 times, say, and
observe 3 heads, then, based on this information, we say that the chance of
e-Self Review