{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# L07_S10 - AMS 311 Lecture 7 Spring 2010 Chapter Three...

This preview shows pages 1–2. Sign up to view the full content.

AMS 311, Lecture 7, Spring 2010 Chapter Three Conditional Probability and Independence 3.2 Conditional Probabilities Definition : If , 0 ) ( F P the conditional probability of E given F , denoted by ) | ( F E P , is . ) ( ) ( ) | ( F P EF P F E P = This definition satisfies the axioms of probability theory. Example 1. From the set of all families with two children, a family is selected at random and found to have a girl. What is the probability that the other child of the family is a girl? Assume that in a two-child family all sex distributions are equally probable. Answer: 1/3. Example 2. From the set of all families with two children, a child is selected at random and is found to be a girl. What is the probability that the second child of this girl’s family is also a girl? Assume that in a two-child family all sex distributions are equally probably. Answer: ½. Law of Multiplication : ). | ( ) ( ) ( F E P F P EF P = The (General) Multiplication Rule : If , 0 ) ( 2 1 N E E E P then ). | ( ) | ( ) | ( ) ( ) ( 1 2 1 1 2 3 1 2 1 1 3 2 1 - - = n n n n E E E E P E E E P E E P E P E E E E E P 3.3.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}