A given blood test has a 98% correct assestment when a patient has a certain dis

Question

A given blood test has a 98% correct assestment when a patient has a certain disease and a 99% correct rate when the patient doesent have the disease. The prevelance of this disease is 1/1200 people.

Use the info to answear the following.

a. Complete the tree diagram

b. Given the tree above, what is the accuracy of this test (what did it get correct?)

c. Suppose that someone has a positive result from the test. What is the probability that they actually have a disease?

DSease Ven ise aSe SeaSe .Seastate P Probs bil ty of 0.Seasc State L+

Explanation / Answer

Ans:

P(positive/desease)=0.98

P(negative/desease)=0.02

P(positive/not desease)=0.01

P(negative/not desease)=0.99

P(desease)=1/1200=0.00083

P(not desease)=0.99917

b)Accuracy =Positive predictive value=P(desease/positive)=0.0008134/(0.0008134+0.0099917)=0.0753

c)P(desease/positive)=P(positive/desease)*P(desease)/[P(positive/desease)*P(desease)+P(positive/not desease)*P(not desease)]

=0.98*0.00083/[0.98*0.00083+0.01*0.99917]

=0.0753

desease not desease Total positive 0.0008134 0.0099917 0.0108 negative 0.0000166 0.9891783 0.9892 Total 0.00083 0.99917 1.0000

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