Stat 491 Chapter 3--Probability

This proportion becomes increasingly close to 1 in 11

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Unformatted text preview: tion becomes increasingly close to 1 in 11 as the number of women sampled increases. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Properties of Probability Prop. 1 For any event A 0 P(A) 1. Prop. 2 If A and B are two events that can not happen at the same time then P(A or B occurs) = P(A) + P(B). Definition Two events A and B are said to be mutually exclusive if they can not happen at the same time. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Example: Properties of Probability Let X be diastolic blood pressure of a person. Let A = {X < 90} and B = {90 X < 95}. Suppose P(A) = 0.7 and P(B) = 0.1. Let C = X < 95. Then, P(C ) = P(A or B) = P(A) + P(B) = 0.7 + 0.1 = 0.8. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests The Complement of an Event The complement of an event A written as A is defined as A = the event that A does not occur = the collection of all outcomes in the sample space that are not in A P(A) = 1 - P(A). Using a venn diagram. Example: For the diastolic blood pressure example where A = {X < 90}, P(A) = 1 - P(A) = 1 - 0.7 = 0.3. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests The Union of Events The union of events A and B written as A B is defined as A B = the event that either A or B or both occur = the collection of all outcomes in the sample space that are either in A or B or both Using a venn diagram Example: For the hypertension example, let A = {X 90} and B = {75 X 100}. Then A B = {X 75}. Chapter...
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This note was uploaded on 10/30/2013 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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