Statistics Notes
Spring 2019

Chapter 3 Probability

§ 3.1 Terminology

  • Probability: a measure of our belief that something will happen.
  • Experimental Probability: `P(E)="number of times event E was observed"/"total number of observations"`
  • Theoretical: `P(E)="favorable outcomes"/"total outcomes"`
  • Experiment: a planned operation carried out under controlled conditions
  • Outcome: the result of an experiment
  • Event: any group of outcomes
  • Simple Event: an event that can’t be reduced to other events
  • Sample Space: all possible simple events
  • Certain Events: `P=1`
  • Impossible Events: `P=0`
  • Complementary Events:`P(barE)=1-P(E)`
    Some people use `E'` to reference the complement of `E`
  • BMCC Students
      Athlete Not Total
    Male 90 310 400
    Female 110 490 600
    Total 200 800 1000
  • Student Grades on Midterm Exam
      A B C Total
    Male 3 10 5 18
    Female 6 17 19 42
    Total 9 27 24 60

§ 3.2 & § 3.3 Independence, Mutually Exclusive, and some Rules

  • Independent Events: `P(A and B)=P(A)P(B)`
  • Mutually Exclusive Events: `P(A or B)=P(A)+P(B)`
  • NON-Mutually Exclusive Events: `P(A or B)=P(A)+P(B)-P(A and B)`
  • Conditional Probability: `P(A | B)=P(A " knowing " B) = (P(A and B))/(P(B))`

§ 3.4 Contingency Tables

  • False Positive: The probability of getting a positive test result, knowing that condition does not actually exist.
    `P("positive test" | "not really") = (P("positve and not really"))/(P("not really"))`
    The chance that you test for “it” but you really don’t have “it”.
  • False Negative: The probability of getting a negative test result, knowing that the condition actually does exist.
  • Testing for Influenza
    Incidence rate = 10%
    False negative rate = 10%
    False Positive rate = 10%
      Positive Negative Total
    Illness 900 100 1000
    No illness 900 8100 9000
    Total 1800 8200 10,000
    a visual contingency table
  • Spreadsheet Example