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Statistics 6.1

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					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



                               AP Statistics, Section 6.1, Part 1   2
The idea of probability
   To understand why we can trust random
    samples and randomized comparative
    experiments, we must look closely at
    chance behavior.




                         AP Statistics, Section 6.1, Part 1   3
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.”




                            AP Statistics, Section 6.1, Part 1   4
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.




                            AP Statistics, Section 6.1, Part 1   5
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



                       AP Statistics, Section 6.1, Part 1   6
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.



                              AP Statistics, Section 6.1, Part 1   7
Simulations
 Cory rolls a die 30 times.
 How often does a number of 2 or less
  appear?




                        AP Statistics, Section 6.1, Part 1   8
Create the random numbers




                AP Statistics, Section 6.1, Part 1   9
Categorize the results




                   AP Statistics, Section 6.1, Part 1   10
Count the results




                    AP Statistics, Section 6.1, Part 1   11
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?




                         AP Statistics, Section 6.1, Part 1   12
300 Trials
 With 300 “rolls”, Emil
  got a number less than
  two, 90 times (30%).
 What was expected?




                 AP Statistics, Section 6.1, Part 1   13
Simulating tossing multiple coins




             AP Statistics, Section 6.1, Part 1   14
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?



                                AP Statistics, Section 6.1, Part 1   15
Assignment
   Exercises: 6.1 - 6.7




                           AP Statistics, Section 6.1, Part 1   16

				
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