Tests for Down syndrome. Currently, there are three

Chapter 3, Problem 80E

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QUESTION:

Problem 80E

Tests for Down syndrome. Currently, there are three diagnostic tests available for chromosome abnormalities in a developing fetus: triple serum marker screening, ultrasound, and amniocentesis. The safest (to both the mother and fetus) and least expensive of the three is the ultrasound test. Two San Diego State University statisticians investigated the accuracy of using ultrasound to test for Down syndrome (Chance, Summer 2007). Let D denote that the fetus has a genetic marker for Down syndrome and N denote that the ultrasound test is normal (i.e., no indication of chromosome abnormalities). Then, the statisticians desired the probability P(D/N). Use Bayes’s Rule and the following probabilities (provided in the article) to find the desired probability: P(D) = 1/180, P(Dc) = 79/80, P(N|D) = 1/2 , P(Nc |D) = 1/2 , P(N|Dc) = 1, and P(Nc |Dc) = 0.

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QUESTION:

Problem 80E

Tests for Down syndrome. Currently, there are three diagnostic tests available for chromosome abnormalities in a developing fetus: triple serum marker screening, ultrasound, and amniocentesis. The safest (to both the mother and fetus) and least expensive of the three is the ultrasound test. Two San Diego State University statisticians investigated the accuracy of using ultrasound to test for Down syndrome (Chance, Summer 2007). Let D denote that the fetus has a genetic marker for Down syndrome and N denote that the ultrasound test is normal (i.e., no indication of chromosome abnormalities). Then, the statisticians desired the probability P(D/N). Use Bayes’s Rule and the following probabilities (provided in the article) to find the desired probability: P(D) = 1/180, P(Dc) = 79/80, P(N|D) = 1/2 , P(Nc |D) = 1/2 , P(N|Dc) = 1, and P(Nc |Dc) = 0.

ANSWER:

Solution:

Step 1 of 2:

It is given that two san Diego state university statisticians investigated the accuracy in using ultrasound to test Down syndrome.

It is also given that D denotes that the fetus has a genetic marker and N denotes that the ultrasound is normal.

We need to find the value of P(D|N) using Bayes’s rule making use of the provided probabilities

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