Question

Problem Nine A test for a certain disease was given to 1,000 subjects, 8% of whom were known to have the disease. For the subjects who had the disease, the test had a positive result for the disease in 90% of the subjects, was inconclusive for 7% and a negative result in 3% of the subjects. For subjects who did not have the disease, the test had a positive result in 5% of subjects, was inconclusive in 10% and a negative result in the remaining 85%.

A. What is the probability of a randomly selected person having the disease given that the test has a positive result?

B. What is the probability of not having the disease given that the test was inconclusive?

Answer 1

From the given information we wnte Positive 90% Negative Inconclusive Total 7%. 87. Disease No disease 31 8 57. SY. 10% 92). Tool -1000 1 Total number of subjects No of subjects whom were known to have disease 80 8 X 1000 100 No. of subjects whom were known to not baring disease 92 - Хооо = 920 loo No. of subject who bad disease and test bad positive result go X80 = 720 loo No. of subject who did not have disease and test hod positive result s X 920 100 5.46

Positive negative Inconclusive Total 2 6 80 Disease No disease Total 72 46 782 92 920 U8 784 98 1000 Probability distribution table is, Negative Õi002 Disease Ne disease Total Positive 0,072 0.046 o.118 Inconclusive Total 0,006 0,08 0,092 0.92 0,098 1 0.782 1 0,784 Probability a randomly A) of selected person having the disease given that the test has a positive result. We know that, PCA 1B) = PCAOB) PCB) :: PC Disease I positive) PChaving disease and positive result) P(positive) 0,072 0118 0,6101

B) Probability of a randomly selected person the disease gived that the test was inconclusive not having P(No disease I In conclusive) = P(not having disease and inconclusive result) P ( In conclusive) o, og2 0,098 0.9387