Question

13. A newly developed DNA diagnostic test can sequence DNA obtained from a mother's blood sample to test whether a fetus is carrying trisomy 21 (which causes Down syndrome). In mothers over 45 the chance of having a child with Down syndrome is 5%. If the test accurately detects trisomy 21 95% of the time and has false positive rate of only 2% (i.e. the fetus is incorrectly diagnosed as having trisomy 21) what is the probability that a child will have Down syndrome if a 16 year old pregnant woman tests positive for the DNA diagnostic test? (15 points)

Answer 1

^%

P(child with Down syndrome above age 45) = 5

^% (accuracy of the test is applicable to both positive and negative results)

P(the test is accurate) = 95

^%

P(the test is false positive) = 2

^{P(46 yr old woman's child has Down syndrome) = 5 +95 – 2 = 98
%}