Chapter 3
Probability
Probability is the tool that allows the statistician to use sample information to make infer
ences about or to describe the population from which the sample was drawn.
3.1
Events, Sample Spaces, and Probability
Definition 3.1 Experiment:
An experiment is the process by which an observation (or
measurement) is obtained.
Definition 3.2 Sample Point:
A sample point is the most basic outcome of an experiment.
Definition 3.3 Sample Space:
The sample space is the set of all possible outcomes (sample
points) of an experiment and is denoted by the symbol
S
.
Example 3.1, page 118
: Two coins are tossed and their up faces are recorded. List of all
sample points for this experiment. Find the sample space S.
See examples for experiments and sample spaces in Table 3.1 on page 119.
Extra Example 1
: Toss a fair coin and through a die. List of all sample points for this
experiment and find the sample space S.
Venn Diagram:
A pictorial method for presenting the sample space where each sample
point is represented by a solid dot and labeled accordingly is called the Venn diagram. See
Figure 3.2, page 120.
Probability:
The probability of a sample point is a number between 0 and 1 that measures
the likelihood that the outcome will occur when the experiment is performed.
Probability Rules for Sample Points:
Let
p
i
represent the probability of a sample point
i
. Then
1. All sample point probabilities must lie between 0 and 1 (0
≤
p
i
≤
1).
2. The probabilities of all the sample points within a sample space must sum to 1 (
∑
i
p
i
= 1).
Example 3.2, page 121.
Example 3.3, page 122.
17
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Definition 3.4 Event:
An event is a specific collection of sample points.
Simple Event:
A single outcome of an experiment is called a simple event.
Compound Event:
A compound event is a collection of simple events.
Probability of an event:
The probability of an event A is equal to the sum of the proba
bilities of the simple events in A.
Example 3.4, page 123
.
Steps for calculating probabilities of events
1. Define the experiment and the type of observation that will be recorded.
2. List the sample points.
3. Assign probabilities to the sample points.
4. Determine the collection of sample points contained in the event of interest.
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 Fall '08
 McGuckian
 Statistics, Probability, Probability theory

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