Suppose a medical test has the following characteristics: Pr(Test +ve Patient Di

Question

Suppose a medical test has the following characteristics: Pr(Test +ve Patient Diseased) = 0.98 Pr(Test-ve | Patient Not Diseased) 0.99 (a) Find Pr(Test -ve | Patient Diseased) and Pr(Test +ve | Patient Not Diseased). Suppose that 1 in 20,000 people have this disease so Pr(Patient Diseased) 0.00005 (b) Compute Pr(Test +ve). Hint: Find Pr(Test +ve, Patient Diseased) and Pr(Test +ve, Patient Not Diseased) (c) Use Bayes' rule to find Pr(Patient Diseasedl Test +ve) (d) Give au ive explamation for the disexepancy be r Patient Diseased | Test +ve) and Pr(Test+ve Patient Diseased).

Explanation / Answer

Ans:

a)Pr(Test -ve/patient diseased)=1-0.98=0.02

Pr(Test +ve/patient not diseased)=1-0.99=0.01

b)Pr(test +ve)=P(test +ve/patient diseased)*P(pateint diseased)+P(test +ve/patient not diseased)*P(pteint not diseased)

=0.98*0.00005+0.01*(1-0.00005)

=0.0100485

c)Pr(Patient diseased/test +ve)=Pr(test +ve/patient diseased)*P(patient diseased)/Pr(test +ve)=(0.98*0.00005)/0.0100485=0.00488

d)Pr(Patient diseased/test +ve) is the probability of a patient diseased given that test is +ve.

(the above prob. is posterior probability)

Pr(Test +ve/patient diseased) is the probability of +ve test given that patient is diseased.

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