Consider the breast cancer example from the lesson. what if the prevalence of br

Question

Consider the breast cancer example from the lesson. what if the prevalence of breast cancer was 15%? Use the table approach to determine the proportion of those testing positive that actually have breast cancer 1 ance 2 Blood donors are usually screened for HIV, both for the safety of the blood supply and for the benefit of the donor. The test, called an ELISA, tests positive 97.5% of the time if the donor actually has HIV. If the donor does not have Hry the EusA test correctly indicates that the person does not have the disease 92.6% of the time. About 02% of college students have HIV. After a blood drive at a college, the lab calls and tells a student that the test has indicated he has HIV. Use what you have learned in this lesson to determine the probability that the student actually has HIV. Because the prevalence of HIV is so small, it may be better to use 100,000 as your total population. A B Considering the answers to questions 1 and 2, should you be more concerned about a positive test for a rare disease or a common disease? Explain your answer. Recently the County Labor and Public Welfare investigated the feasibility of setting up a county wide screening program to detect child abuse. A team of consultants estimated the following probabilities: . 1 child in 90 is abused. A physician can detect an abused child 90% of the time. A screening program would incorrectly label 3% of all non-abused children as abused. * A. What is the probability that a child is actually abused given that the screening program diagnosed this child as abused? B. How does the answer in part A change if the incidence of abuse is 1 in 1000?

Explanation / Answer

Solution-

Let the events are-

A- Child is actually abused.

N- Child is not abused

D- Labelled as abused

Given probabilities are-

P(A) = 1/90 and P(N) = 89/90

P(D|A) = 0.9 and P(D|N) = 0.03

(A) P(A|D)

= P(A) * P(D|A) / [ P(A) * P(D|A) + P(N) * P(D|N) ] { using bayes theorem }

= 1/90 * 0.9 / [ 1/90 * 0.9 + 89/90 * 0.03]

= 0.2521

(B) Now, P(A) 1/1000

SO Answer would be-

= P(A) * P(D|A) / [ P(A) * P(D|A) + P(N) * P(D|N) ] { using bayes theorem }

= 1/1000 * 0.9 / [ 1/1000 * 0.9 + 999/1000 * 0.03]

= 0.02916

Answers

TY!

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