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Let's continue with the previous scenario: 0.03 0.97 Y N Y Dc 0.98 N D 0.99 0.01 0.02 i) The probability of having the disease and testing positive is P(DNY)=P(D) P(Y|D) = Number ii) The probability of not having the disease and testing positive is P(DCnY) = P(DC) P(Y|DC) = Number iii) The total probability of testing positive is, by the Total Probability Rule, the sum of these, namely P(Y) = P(D) P(Y|D) + P(DC) P(Y|DC) = Number

Let's continue with the previous scenario: 0.03 0.97 Y N Y Dc 0.98 N D 0.99 0.01 0.02 i) The probability of having the disease and testing positive is P(DNY)=P(D) P(Y|D) = Number ii) The probability of not having the disease and testing positive is P(DCnY) = P(DC) P(Y|DC) = Number iii) The total probability of testing positive is, by the Total Probability Rule, the sum of these, namely P(Y) = P(D) P(Y|D) + P(DC) P(Y|DC) = Number

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let's continue with the previous scenario: 0.03 0.97 D 0.99. Y 0.01 N 0.02 Y DC 0.98 N i) The probability of having the disease and testing positive is P(DnY)=P(D) P(Y|D) = Number ii) The probability of not having the disease and testing positive is P(DC Y) = P(DC) P(Y|DC) = Number iii) The total probability of testing positive is, by the Total Probability Rule, the sum of these, namely P(Y) = P(D) P(Y|D) + P(DC) P(Y|DC) = Number The conditional probability of D given Y is, by Bayes' Rule, P(Dn Y) P(Y) P(DY) = Number So there is roughly a 40% chance that you do not have the disease even if you do test positive for it. This is an important and perhaps surprising result that is worth understanding: just because you test positive for something does not guarantee that you actually have it. Note: your answers should be entered with at least 2 significant figures of accuracy.
Transcribed Image Text:Let's continue with the previous scenario: 0.03 0.97 D 0.99. Y 0.01 N 0.02 Y DC 0.98 N i) The probability of having the disease and testing positive is P(DnY)=P(D) P(Y|D) = Number ii) The probability of not having the disease and testing positive is P(DC Y) = P(DC) P(Y|DC) = Number iii) The total probability of testing positive is, by the Total Probability Rule, the sum of these, namely P(Y) = P(D) P(Y|D) + P(DC) P(Y|DC) = Number The conditional probability of D given Y is, by Bayes' Rule, P(Dn Y) P(Y) P(DY) = Number So there is roughly a 40% chance that you do not have the disease even if you do test positive for it. This is an important and perhaps surprising result that is worth understanding: just because you test positive for something does not guarantee that you actually have it. Note: your answers should be entered with at least 2 significant figures of accuracy.
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