Conditional Probability, Total Probability Theorem and ... - Berlin Chen

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Inference Using Bayes’ Rule (1/2)惡性腫瘤Figure 1.14:良性腫瘤Probability-Berlin Chen 20
Inference Using Bayes’ Rule (2/2)• Example 1.18. The False-Positive Puzzle.– A test for a certain disease is assumed to be correct 95% of the time: ifa person has the disease, the test with are positive with probability 0.95( PBA 0. 95 ), and if the person does not have the disease, the testresults are negative with probability 0.95 ( cP B c A 0 .95 ). A random person drawn from a certain population has probability 0.001( P A0 . 001 ) of having the disease. Given that the person just testedpositive, what is the probability of having the disease ( P A B ) ?• A : the event that the person has a disease• B : the event that the test results are positivePABPPAPBP BPAAPccAPBA P APBA BAP BAc1 c c P B A 0 .050 .0010 .001 0 .95 0 .95 0 .9990 .050 .0187Probability-Berlin Chen 21
Page 1 and 2: Conditional Probability, Total Prob
Page 3 and 4: Conditional Probability (2/2)• Wh
Page 5 and 6: Conditional Probabilities Satisfy G
Page 7 and 8: Simple Examples using Conditional P
Page 9 and 10: Using Conditional Probability for M
Page 11 and 12: Multiplication (Chain) Rule• Assu
Page 13 and 14: Multiplication (Chain) Rule: Exampl
Page 15 and 16: Total Probability Theorem (2/2)Figu
Page 17 and 18: Some Examples Using Total Probabili
Page 19: Bayes’ Rule• Let A 1, A2,,A n b
Page 23: Homework -1• Chapter 1 : Addition

Conditional Probability, Total Probability Theorem and ... - Berlin Chen

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