AP Statistics Curriculum 2007 Prob Rules
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:<math>P(A | B) ={P(A \cap B) \over P(B)}.</math> | :<math>P(A | B) ={P(A \cap B) \over P(B)}.</math> | ||
+ | ===Example=== | ||
+ | Here is the data on 400 Melanoma (skin cancer) Patients by Type and Site | ||
+ | <center> | ||
+ | {| class="wikitable" style="text-align:center; width:75%" border="1" | ||
+ | |- | ||
+ | | Site | ||
+ | |- | ||
+ | | Type || Head and Neck || Trunk || Extremities || Totals | ||
+ | |- | ||
+ | | Hutchinson's melanomic freckle || 22 || 2 || 10 || 34 | ||
+ | |- | ||
+ | | Superficial || 16 || 54 || 115 || 185 | ||
+ | |- | ||
+ | | Nodular || 19 || 33 || 73 || 125 | ||
+ | |- | ||
+ | | Indeterminant || 11 || 17 || 28 || 56 | ||
+ | |- | ||
+ | | Column Totals || 68 || 106 || 226 || 400 | ||
+ | |} | ||
+ | </center> | ||
Revision as of 04:08, 29 January 2008
Contents |
General Advance-Placement (AP) Statistics Curriculum - Probability Theory Rules
Addition Rule
The probability of a union, also called the Inclusion-Exclusion principle allows us to compute probabilities of composite events represented as unions (i.e., sums) of simpler events.
For events A1, ..., An in a probability space (S,P), the probability of the union for n=2 is
For n=3,
In general, for any n,
Conditional Probability
The conditional probability of A occurring given that B occurs is given by
Example
Here is the data on 400 Melanoma (skin cancer) Patients by Type and Site
Site | ||||
Type | Head and Neck | Trunk | Extremities | Totals |
Hutchinson's melanomic freckle | 22 | 2 | 10 | 34 |
Superficial | 16 | 54 | 115 | 185 |
Nodular | 19 | 33 | 73 | 125 |
Indeterminant | 11 | 17 | 28 | 56 |
Column Totals | 68 | 106 | 226 | 400 |
Multiplication Rule
Model Validation
Checking/affirming underlying assumptions.
- TBD
Computational Resources: Internet-based SOCR Tools
- TBD
Examples
Computer simulations and real observed data.
- TBD
Hands-on activities
Step-by-step practice problems.
- TBD
References
- TBD
- SOCR Home page: http://www.socr.ucla.edu
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