AP Statistics Curriculum 2007 Prob Rules

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.

Venn Diagrams

For events A₁, ..., A_n in a probability space (S,P), the probability of the union for n=2 is \[P(A_1\cup A_2)=P(A_1)+P(A_2)-P(A_1\cap A_2),\]

For n=3, \[P(A_1\cup A_2\cup A_3)=P(A_1)+P(A_2)+P(A_3) -P(A_1\cap A_2)-P(A_1\cap A_3)-P(A_2\cap A_3)+P(A_1\cap A_2\cap A_3)\]

In general, for any n, \[P(\bigcup_{i=1}^n A_i) =\sum_{i=1}^n P(A_i) -\sum_{i,j\,:\,i<j}P(A_i\cap A_j) +\sum_{i,j,k\,:\,i<j<k}P(A_i\cap A_j\cap A_k)+ \cdots\cdots\ +(-1)^{j+1} P(\bigcap_{i=1}^j A_i)+ \cdots\cdots\ +(-1)^{n+1} P(\bigcap_{i=1}^n A_i).\]

Conditional Probability

The conditional probability of A occurring given that B occurs is given by \[P(A | B) ={P(A \cap B) \over P(B)}.\]

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

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

---

---

Translate this page:

(default)	Deutsch	Español	Français	Italiano	Português	日本語	България	الامارات العربية المتحدة	Suomi	इस भाषा में	Norge
한국어	中文	繁体中文	Русский	Nederlands	Ελληνικά	Hrvatska	Česká republika	Danmark	Polska	România	Sverige