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

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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.
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