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)=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 |
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))`
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