Transcript A.P. STATISTICS LESSON 6

AP STATISTICS
LESSON 6 - 1
THE IDEA OF PROBABILITY
ESSENTIAL QUESTION:
How is probability used in
Statistics?
Objectives:
 To develop a working understanding of
Probability.
 To understand what is meant by
“Random,” and what it’s characteristics are
in the long run.
Introduction
Probability is a branch of mathematics that
describes the pattern of chance outcomes.
The reasoning of statistical inference rests
on asking, “ How often would this method
give a correct answer if I used it many,
many times?”
The Idea of Probability
 Probability begins with the observed fact that
some phenomena are random – that is , the
relative frequencies of their outcomes seem to
settle down to fixed values in the long run.
 The big idea is this: chance behavior is
unpredictable in the short run but has a regular
and predictable pattern in the long run.
 The tossing of a coin can not be predicted in just
a few flips, but there is a regular pattern in the
results, a pattern that emerges clearly only after
many repetitions.
Example 6.1
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COIN TOSSING
For the first few tosses the proportion of
heads fluctuates quite a bit, but settles
down as we make more and more tosses.
Randomness and Probability
Randomness in statistics is not a synonym
for “haphazard” but a description of a kind
of order that emerges only in the long run.
The idea of probability is empirical. That
is, it is based on observation rather than
theorizing.
Randomness and Probability
(definitions)
 We call a phenomenon random if individual
outcomes are uncertain but there is nonetheless
a regular distribution of outcomes in a large
number of repetitions.
 The probability of any outcome of a random
phenomenon is the proportion of times the
outcome would occur in a very long series of
repetitions. That is, probability is long – term
relative frequency.
Thinking about Randomness
 That some things are random is an
observed fact about the world.
 Independent – The outcome of one trial
must not influence the outcome of any
other.