Chapter 5: Probability

Section 5.1: Probability Rules

Knowledge Prerequisites

declarative knowledge (definitions)
1. none
procedural knowledge
1. none
conditional knowledge
1. none

Learning Goals

declarative knowledge (definitions)
1. probability
2. outcome
3. law of large numbers
4. [probability] experiment
5. sample space, S
6. random event
7. probability rules
8. probability model
9. unusual event
10. empirical [a.k.a., frequentist] probability
11. equally-likely outcomes
12. classical [a.k.a., classicist] probability
13. subjective probability
14. fair coin, fair die
procedural knowledge
1. verify probability models
2. write complete sample space for a given situation
3. use complete sample space to calculate probabilities using classical approach
4. calculate probabilities using classicist approach
5. approximate probabilities using frequentist approach
6. construct a probability model using given data
conditional knowledge
1. know when it is appropriate to use the concept of probability
2. know the importance of the concept of randomness or chance in probability
3. interpret value of probability
4. know the difference between classicist and frequentist approaches
5. know when to use classicist or frequentist approach
6. understand why the empirical approach only results in approximate probabilities
7. identify when an event is considered unusual
important notes
1. tests will not include questions on playing cards or roulette
2. answers must be in complete sentences using the correct symbols, e.g., P(x = hearts) = 1/4
3. answers to probability questions can be in any of the following form: unreduced fraction, reduced fration, decimal, or percentage

Section 5.2: The Addition Rule and Complements

Knowledge Prerequisites

declarative knowledge (definitions)
1. Section 5.1:
  - probability
  - outcome
  - sample space, S
  - random event
  - probability model
  - unusual event
procedural knowledge
1. Section 5.1:
  - use complete sample space to calculate probabilities using classical approach
  - calculate probabilities using classicist approach
conditional knowledge
1. Section 5.1:
  - know when it is appropriate to use the concept of probability
  - know the importance of the concept of randomness or chance in probability
  - interpret value of probability
  - identify when an event is considered unusual

Learning Goals

declarative knowledge (definitions)
1. disjoint [a.k.a., mutually-exclusive] events
2. Venn diagrams
3. addition rule for probability
4. general addition rule for probability
5. contingency table [a.k.a., two-way table]
6. complement of an event, E^c
7. complement rule for probabilities
8. keywords for probability:
  1. or
  2. and [sometimes you will need to identify and even though word is not used]
  3. not
procedural knowledge
1. how to calculate the probability of an event using the addition rule
2. how to calculate the probability of an event using the general addition rule
3. how to calculate the probability of an event using the complement rule
4. how to calculate the probability of an event from a contingency table
5. know how to use algebra to rearrange any probability rule to solve for an unknown quantity
conditional knowledge
1. how to determine which probability rule to use for a given problem
2. how to determine if two events are disjoint
3. how to identify the complement of an event
4. know that probability, proportion, and percentage are equivalent
important notes
1. tests will not include questions on playing cards or roulette
2. answers must be in complete sentences using the correct symbols, e.g., P(x = hearts) = 1/4
3. answers to probability questions can be in any of the following form: unreduced fraction, reduced fration, decimal, or percentage

Section 5.3: Independence and the Multiplication Rule

Knowledge Prerequisites

declarative knowledge (definitions)
1. Section 5.1:
  - probability
  - outcome
  - sample space, S
  - random event
  - probability model
  - unusual event
procedural knowledge
1. Section 5.1:
  - calculate probabilities using classicist approach
conditional knowledge
1. Section 5.1:
  - know when it is appropriate to use the concept of probability
  - know the importance of the concept of randomness or chance in probability
  - interpret value of probability
  - identify when an event is considered unusual

Learning Goals

declarative knowledge (definitions)
1. independent events
2. multiplication rule for probability
procedural knowledge
1. how to calculate the probability of an event using the multiplication rule
conditional knowledge
1. understand that independence events and disjoint events are different concepts
2. understand that independence events and disjoint events are different concepts
3. understand when repititions of a random phenomenom are independent, the probability of future events does not change
4. how to use the multiplication rule for a given problem
5. know how to use algebra to rearrange any probability rule to solve for an unknown quantity
important notes
1. tests will not include questions on playing cards or roulette
2. answers must be in complete sentences using the correct symbols, e.g., P(x = hearts) = 1/4
3. answers to probability questions can be in any of the following form: unreduced fraction, reduced fration, decimal, or percentage

Section 5.4: Conditional Probability and the General Multiplication Rule

Knowledge Prerequisites

declarative knowledge (definitions)
1. Section 5.1:
  - probability
  - outcome
  - sample space, S
  - random event
  - probability model
  - unusual event
2. Section 5.3:
  - independent events
  - multiplication rule for probability
procedural knowledge
1. Section 5.1:
  - calculate probabilities using classicist approach
conditional knowledge
1. Section 5.1:
  - know when it is appropriate to use the concept of probability
  - know the importance of the concept of randomness or chance in probability
  - interpret value of probability
  - identify when an event is considered unusual
2. Section 5.3:
  - understand that independence events and disjoint events are different concepts
  - conceptually identify if two events are independent
  - know how to use algebra to rearrange any probability rule to solve for an unknown quantity

Learning Goals

declarative knowledge (definitions)
1. keyword for probability:
  1. given that [sometimes you will need to identify given that even though word is not used]
2. conditional probability
3. general multiplication rule for probability
4. N(E)
procedural knowledge
1. how to calculate the probability of an event using the conditional probability rule
2. how to calculate the probability of an event using the general multiplication rule
3. how to calculate the conditional probability from values in a contingency table
4. how to use the general multiplication rule to calculate the probability from values in a contingency table
5. how to use conditional probability to determine if two events are independent, i.e., if P(F|E) = P(F)
conditional knowledge
1. how to identify which probability rule to use for a given problem
2. identify the difference between P(E) and N(E)
3. how to use the conditional probability rule for a given problem
4. how to use the general multiplication rule for a given problem
5. know how to use algebra to rearrange any probability rule to solve for an unknown quantity
important notes
1. tests will not include questions on playing cards or roulette
2. answers must be in complete sentences using the correct symbols, e.g., P(x = hearts) = 1/4
3. answers to probability questions can be in any of the following form: unreduced fraction, reduced fration, decimal, or percentage
4. P(at least 1) = 1 – P(none)

Chapter 5: Required Formulas – Need to Know for Tests

Approximating Probabilities Using the Empirical Approach:
Approximating Probabilities Using the Classical Method:
Addition Rule for Disjoint Events: P(E or F) = P(E) + P(F)
General Addition Rule: P(E or F) = P(E) + P(F) – P(E and F)
Complement Rule for Disjoint Events: P(E^C) = P(not E) = 1 – P(E)
Multiplication Rule for Independent Events: P(E and F) = P(E) * P(F)
Conditional Probability Rule: