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