Stat 491 Chapter 3--Probability

# Then the conditional probability of event a given

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: P(A|B), is defined as P(A|B) = P(A B) P(B) and the conditional probability of event B given event A is defined in similar way assuming that P(A) > 0. Using a venn diagram. If A and B are independent then P(B|A) = P(B) = P(B|A). Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Relative Risk The relative risk (RR) of B given A is RR = Obviously, 0 RR < . Clearly, if A and B are independent then RR = 1. The more the dependence between events increase, the further the RR will be from 1. P(B|A) . P(B|A) Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Relative Risk: Example Suppose that 1500 smokers in 10,000 develop lung cancer in 20 years and 50 non-smokers in 5000 developed lung cancer in 20 years. What is the relative risk of lung cancer in 20 years given a person smokes? Let A = {Smoker} and B = {Develop lung cancer}. Then RR = P(B|A) 0.15 = 0.01 = 15. P(B|A) Therefore, smokers are 15 times more likely to develop lung cancer in 20 years than nonsmokers. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Total Probability Rule Let A and B be any two events. Clearly, P(B) = P(B A) + P(B A). The above relation implies P(B) = P(B|A) P(A) + P(B|A) P(A) which is known as the Total Probability Rule. Generalization of the total probability rule: Let A1 , A2 , , Am be a set of mutually exclusive and exhaustive events. Then, m P(B) = i=1 Chapter 3: Probability P(B|Ai ) P(Ai ). Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Total Probability Rule: Example Suppose the rate of type II diabetes mellitus (DM) in 40- to 59-year old is 7% among Caucasians, 10% among African Americans, 12% among Hispanics and 5% among Asian Americans. Suppose the ethnic distribution in Houston, TX is 30% Caucasian, 25% African American, 40% Hispanic...
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