Dave's Web Corner

MTH-208 Week 4 (January 29-February 4)

recommended:
- Chapter 3 Practice (pp. 164-166): 1-39
- Chapter 3 Homework (p. 168): 1-2
an experiment is a specific procedure carried out under well-defined conditions, if the result is not pre-determined the experiment is called a chance experiment.
an outcome is the result of an experiment
the sample space of an experiment is the set of all possible outcomes of the experiment
an event is any combination of outcomes
Probability can be calculated exerimentally or theoretically
- the experimental probability of an outcome is the long-term frequency of that outcome (how many times the outcome occurs divided by how many times the experiment is conducted
- the theoretical probability of an outcome the number of ways that the outcome can occur divided by the total number of outcomes possible
- either way, the probability of an outcome must be a number between \( 0 \) and \( 1 \).
  - a probability of \(0\) means that the outcome cannot occur or never occurs
  - a probability of \(1\) means that the the outcome must occur or always occurs
outcomes can combined with key words to form more complex outcomes, if \( A \) and \( B \) are events
- \( A \) and \( B \) is the event where both \( A \) and \( B \) occur
- \( A \) or \( B \) is the event where either \( A \), or \( B \), or both \( A \) and \( B \) occur
- \( A' \), the complement of \( A \), is the event where \( A \) does not occur
- \( A|B \) is the event where \( A \) occurs given that \( B \) has occurred

recommended:
- Chapter 3 Practice (p. 166): 40-43
- Chapter 3 Homework (pp. 168-169): 3-14
independent events
- events \( A \) and \( B \) are called independent if the knowledge that one of the events has occurred does change the probability that the other event will occur, mathematically this is the same as any one of the following three statements
  - \( P(A|B)=P(A) \)
  - \( P(B|A)=P(B) \)
  - \( P(A \mbox{ and } B)=P(A)P(B) \)
- if any one of these equations is true then \( A \) and \( B \) are independent events
- if \( A \) and \( B \) are not independent events, then they are called dependent events
- when sampling with and without replacement
  - with replacement events of choosing elements are considered to be independent
  - without replacement events of choosing elements are considered to be dependent
  - when in doubt assume events are dependent unless you can show otherwise
mutually exclusive events
- events \( A \) and \( B \) are called mutually exclusive the cannot both occur at the same time, that is \( P(A \mbox{ and } B)=0 \)

recommended:
- Chapter 3 Practice (p. 166): 44-53
- Chapter 3 Homework (pp. 169-173): 15-35
recommended: 44-53, 80-100
the multiplication rule
- in general
  - \( P(A\mbox{ and }B)=P(A|B)P(B) \)
- if \( A \) and \( B \) are independent, that is if \( P(A|B)=P(A) \), then
  - \( P(A\mbox{ and }B)=P(A)P(B) \)
the addition rule
- in general
  - \( P(A\mbox{ or }B)=P(A)+P(B)-P(A\mbox{ and }B) \)
- if \( A \) and \( B \) are mutually exclusive, that is if \( P(A\mbox{ and }B)=0 \), then
  - \( P(A\mbox{ or }B)=P(A)+P(B) \)

recommended:
- Chapter 3 Practice (p. 166): 54-57
- Chapter 3 Homework (pp. 174-175): 35-48
recommended: 54-57, 101-113
a contingency table is a useful method for organizing basic data and calculating conditional probabilities
contingency tables can help us decide if events are dependent, or contingent on each other, that is where the name contingency table came from
contingency tables may be filled in with frequencies or probabilities (relative frequencies)
it is helpful to add a "totals" row and "totals" column to your contingency tables

Calendar of all assessments and deadlines (XYZ and written homework, exams)
Homework
- XYZ Homework
  - Completed at https://www.xyzhomework.com
- Written Homework
  - Submitted Mondays and Wednesdays by 11:59pm as a single PDF file to our MTH-208W Assignments folder.
Exams
- Exam 1: in class Wednesday, February 15
  - Exam 1 (solutions)
  - Exam 1 covers chapters 1-4
Schedule
- Week 4
  - Written Homework 5, due Monday, January 30
    - Problems 8, 9
  - Written Homework 6, due Wednesday, February 1
    - Problem 10
  - XYZ Homework Sections 3.1-3.4, due Saturday, February 4
- Week 5
  - Written Homework 7, due Monday, February 6
    - Problems 11, 12
  - Written Homework 8, due Wednesday, February 8
    - Problems 13
  - XYZ Homework Sections 3.5, due Saturday, February 11
  - XYZ Homework Sections 4.1-4.3, due Saturday, February 11
- Week 6
  - Written Homework 9, due Monday, February 13
    - Problems 14, 15
  - Exam 1, Wednesday, February 15
  - XYZ Homework Section 5.1, due Saturday, February 18