Statistics Notes
Spring 2019
Chapter P Probability
§ P.1 Probability Basics
 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)=1P(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 
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)`
 NONMutually 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))`
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 
 Spreadsheet Example