The goal of statistics:
In order to use the sample to draw inferences or make conclusions about
the population we need to understand
probability
.
Probability
Probability
is a numerical measure of the likelihood that an event will occur.
Examples
:
Experiment
: a process that generates well deﬁned outcomes.
Only one of the possible outcomes occurs on a single repetition of the ex
periment.
Examples
:
1
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: the set of all outcomes
Examples
:
Often in order to discuss probabilities of outcomes we need to know how
many possible outcomes there are.
Counting rules for Outcomes
1.
Multistep Experiments
Ex
: Tossing two coins
2. Suppose an experiment can be described as a sequence of
k
steps. Let
n
1
be the number of possible outcomes for step 1,
n
2
be the number of
possible outcomes for step 2, etc. Then
Total number of outcomes =
n
1
n
2
···
n
k
.
Ex
: In the city of Milford, applications for zoning changes go through a
twostep process: a review by the planning commission and a ﬁnal deci
sion by the city council. At step 1 the planning commission reviews the
zoning change request and makes a positive, neutral, or negative recom
mendation. At step 2 the city council reviews the planning commission’s
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 Fall '10
 Jager,AbigailL
 Statistics, Probability, Probability theory, Trigraph, B unit

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