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?

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)

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