AP Statistics
Clifton 1 Chapter 6 – Probability Notetaking Guide
Section 6.1 – Chance Experiments and Events •
Chance Experiments
How is a chance experiment different than a scientific experiment?
How many outcomes must a chance experiment have?
What is a sample space?
Give an example of a chance experiment and define its sample space.
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Events
What is the difference between an event and a simple event?
What are the key features of a Venn diagram?
What does it mean for two events to be disjoint or mutually exclusive?
Homework # 3, 5, 8, 9, 11, 12
AP Statistics Section 6.2 – Definition of Probability •
Classical Approach of Probability
What is the earliest evidence of games of chance?
Which mathematicians help formalize the study of probability and when did they live?
What are the limitations of the classical approach for calculating probability?
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Relative Frequency Approach to Probability
What is the Law or Large Numbers and how does it relate to the calculation of probabilities?
How does the relative frequency approach differ from the classical approach to probability calculations?
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Subjective Approach to Probability
Summarize this section in your own words. Why do you think it was included in the text?
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How Are Probabilities Determined?
How will the principles of this section help you process probability information?
Clifton 2
AP Statistics
Clifton 3
Section 6.3 – Basic Properties of Probability List the fundamental properties of probability and provide examples of events that illustrate each property: 1. 2. 3. 4. •
Equally Likely Outcomes
Give three examples of chance experiments that have equally likely outcomes.
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Addition Rule for Disjoint Events
Why is it that the addition rule given here can only be applied to mutually exclusive events?
Homework #16, 21, 23, 24, 26, 28, 29 Section 6.4 – Conditional Probability Explain the concept of conditional probability in your own words. What is the condition?
Illustrate how the calculation of a conditional probability is performed using both a table and a corresponding Venn diagram.
Homework # 31, 32, 35, 37, 38, 40, 42
AP Statistics
Clifton 4
Section 6.5 – Independence Explain why the events must be independent if the conditional probability is equal to the probability of a given event occurring.
Use probability statements to derive the Multiplication Rule from the definition of independent events.
Extend the above to get the Multiplication Rule for k Independent Events.
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Sampling With and Without Replacement
Give an example of sampling with replacement.
Give an example of sampling without replacement.
Why is it justifiable to assume samples are independent if the sample size is not larger than 5% of the population?
Homework # 43, 46, 47, 50, 51, 54, 55
AP Statistics
Clifton 5
Section 6.6 – Some General Probability Rules •
General Addition Rule
Explain the General Addition Rule in your own words.
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General Multiplication Rule
The General Multiplication Rule follows from an important definition. What is it and how does it relate?
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Law of Total Probability
In your own words explain the Law of Total Probability.
Why is it essential that the events be disjoint?
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Bayes’ Rule
Illustrate the application of Bayes’ Rule by using a tree diagram to represent the events from example 6.27 Lyme Disease.
Homework # 59, 61, 63, 65, 66, 74, 76, 77
AP Statistics Section 6.7 – Estimating Probabilities Empirically Using Simulation •
Estimating Probabilities Empirically
How are the probabilities estimated empirically?
What is the role of conditional probability in the empirical estimation process?
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Estimating Probabilities Using Simulation
Name at least two methods for performing a simulation.
How is the estimate of a given probability obtained through simulation?
Homework #78, 81, 82, 84, 87, 88, 93, 95, 98, 101, 102
Clifton 6