Transcript probability

Section 6.1.1
The Idea of Probability
Statistics
Probability is studied…

When looking at games of chance
◦ cards, dice, lotteries

When looking at social science data
◦ Life, death

When looking at scientific data
◦ Variations in individual measurement are
random
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The idea of probability

To understand why we can trust random
samples and randomized comparative
experiments, we must look closely at
chance behavior.
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Random is not “haphazard”

The Big Idea: “Chance behavior is
unpredictable in the short run but has a
regular and predictable pattern in the long
run.”
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Definition of Random

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.
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Definition of Probability
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 frequency.
 Computer simulations can allows us to
see those long-term frequencies

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Independence
In order for an event to be considered
random, it must be independent.
 That is, it must not be influenced by other
(perhaps previous) events.
 Example:

◦ Flipping a head does not make it more
probable that a tail will occur next.
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Simulations
Cory rolls a die 30 times.
 How often does a number of 2 or less
appear?

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Create the random numbers
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Categorize the results
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Count the results
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Consider
During the last simulation, Cory “rolled”
numbers two or less 11 times. (36.7%)
 Is this what you expected?
 Why wasn’t it exactly 10.
 What would happen if Cory “rolled” 300
times?

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300 Trials
With 300 “rolls”, Emil
got a number less than
two, 90 times (30%).
 What was expected?

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Simulating tossing multiple coins
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What about things you can’t “simulate”

Spin a penny on your desk.
◦ How many times does it fall heads up?
◦ What is the probability that it fall heads up?

Toss a thumbtack on a hard surface 100
times.
◦ How times did it lands point up?
◦ What is the probability that it lands point up?
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Assignment

Exercises: 6.1 - 6.7
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