Stat 491 Chapter 3--Probability

# This result is not unexpected why chapter 3

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Multiplication and Addition Laws Multiplication Law: For mutually independent events A1 , A2 , . . . , Am , P(A1 A2 Am ) = P(A1 ) P(A2 ) P(Am ). Addition Law: For any two events A and B, P(A B) = P(A) + P(B) - P(A B). Use venn diagram. For the STD example, suppose a patient will be referred for further lab test if at least one of the doctors makes a positive diagnosis. Then P(A+ B + ) = P(A+ )+P(B + )-P(A+ B + ) = 0.1+0.17-0.08 = .19 Thus 19% of all patients will be referred for further lab tests. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Addition Law for Independent Events If A and B are independent events then P(A B) = P(A) + P(B)[1 - P(A)]. Example: Let A = {Wife's DBP > 95} and B = {Husband's DBP > 95} where DBP stands for diastolic blood pressure. Assume that P(A) = 0.1 and P(B) = 0.2. Then the probability of a hypertensive household is P(AB) = P(A)+P(B)[1-P(A)] = 0.1+0.2[1-0.1] = 0.28. Therefore, 28% of all households will be hypertensive. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Addition Law for More Than Two Events For any events A, B and C , P(A B C ) = P(A) + P(B) + P(C ) - P(A B) - P(A C ) - P(B C ) + P(A B C ) The addition law also generalizes to an arbitrarily number of events, although that is beyond the scope of this course. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Conditional Probability Let A and B be two events with P(B) > 0. Then the conditional probability of event A given event B, written as...
View Full Document

## This note was uploaded on 10/30/2013 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

Ask a homework question - tutors are online