A laboratory test for the detection of a certain disease gives a positive result

Question

A laboratory test for the detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease The test gives a negatisve result 0.3 percent of the time for people who have the disease. Large-scale studies have shown that the disease occurs in about 2 percent of the population. What is the probability that a person selected at random would test positive for this disease? Show your work. What is the probability that a person selected at random who tests positive for the disease does not have the disease? Show your work. using the info in #3 on the multiple choice, are the events "4 or more credit cards" and "owning home less than 1 year" independent?

Explanation / Answer

Answer)

Events:- A: Detection gives positive result

B: Detection gives negative result

C: disease occurs

D: disease doesnot occur

Given: P(A|D) = 0.05; P(B|C)= 0.003; P(C) = 0.02; P(D) = 1-P(C) = 1-0.02= 0.98

(a) P(A) = P(A|D)P(D) + P(A|C)P(C) = (0.05*0.98)+(1-0.003)*0.02 = 0.06894

(b) P(D|A) = P(D)P(A|D)/P(A) = (0.98*0.05)/0.06894 = 0.711

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