# Statistics 6.1

Document Sample

```					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

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 11 posted: 3/13/2012 language: pages: 16