1. Section 6.1 The Idea of Probability
Honors Statistics
November 10th, 2014
Mr. Calise

2. 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

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

11. AP Statistics, Section 6.1, Part 1
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. AP Statistics, Section 6.1, Part 1
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. AP Statistics, Section 6.1, Part 1
Assignment
Exercises: 6.1, 6.3, 6.5, 6.7, 6.10
AP Statistics, Section 6.1, Part 1