Question

Suppose a rare, but fatal, disease affects 1 person in n. Researchers have developed a powerful diagnostic test for this disease, but it has a margin of error. Everyone who has the disease will test positive, but B E (0,1) who do not have the disease will also test positive. This implies that 1-β who do not have the disease will test negative for the disease. In other words, the test will produce some false positives. Fran Seen recently tested positive for the disease during a routine physical, she was horrified. Fran was recently advised about a surgical procedure (fully covered by her insurance) that would certainly eliminate the disease if she has it. There is a risk, however, that she dies with probability a e (0,1) because of complications during the surgery. Before doing any calculations, do you think that undergoing the surgery would increase Fran's overall probability of survival? Suppose an overall population of m people where m > n. a. b. i. What is the number of people who have the disease? i. Suppose everybody is tested, what is the approximate number of people who will test positive for the disease? What is the fraction of people who actually have the disease? 1. What then is the probability that Fran has the disease? 2. Would Fran improve her survival probability by undergoing surgery? Explain a. Suppose the chance of dying during surgery depends on the number of people who have already had the surgery Let y (0.1) be the percent of those people with the disease that have been operated on such that the probability of dying becomes: c. y (your answer to pert(b.m i. How does δ depend on n.), and m? Explain and show your answer(s) i. Would Fran improve her survival probability by undergoing surgery? Explain.

I believe I have obtained the correct answers for this, however,

I just want to make sure I did the steps correctly. Any help is appreciated, Thank You!

oops, sorry! parts b & c (all parts)

Answer 1

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