Sarah Jessica Parker is 39. As a "mature" mother, she is worried about the possibility of having a baby with Down Syndrome. Chances of a 39-year old mother having a baby with Down Syndrome is approximately 1 in 100. Just to be on the safe side, Sarah decides to have a maternal blood serum test to check for chromosomal abnormalities. If the baby has Down Syndrome, then the blood serum test will deliver a positive result 90% of the time. There is, however, a small "false positive" rate of 7%. I want you to explain all of this using simple numbers that any layperson can get his/her head around.
Suppose 1000 39-year old mothers choose to get the maternal blood serum test. (a) How many mothers will get a "true positive", i.e. the baby has DS and the test returns a positive result? (b) How many will get a "false positive", i.e. the baby does not have DS, but the test returns a positive result? (c) How many mothers will get a "false negative", i.e. the baby has DS, but the test returns a negative result? (d) Suppose Sarah gets a positive test result. Using only the numbers you have found in the previous parts of this question, what is the posterior probability that her baby has Down Syndrome? How much larger is this compared to her prior probability?

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The Answer of Sarah Jessica Parker is 39. As a "mature" mother, she is worried about the possibility of having a baby with Down Syndrome. Chances of a 39-year old mother having a baby with Down Syndrome is approximately 1 in 100. Just to be on the safe side, Sarah decides to have a maternal blood serum test to check for chromosomal abnormalities. If the baby has Down Syndrome, then the blood serum test will deliver a positive result 90% of the time. There is, however, a small "false positive" rate of 7%. I want you to explain all of this using simple numbers that any layperson can get his/her head around.
Suppose 1000 39-year old mothers choose to get the maternal blood serum test. (a) How many mothers will get a "true positive", i.e. the baby has DS and the test returns a positive result? (b) How many will get a "false positive", i.e. the baby does not have DS, but the test returns a positive result? (c) How many mothers will get a "false negative", i.e. the baby has DS, but the test returns a negative result? (d) Suppose Sarah gets a positive test result. Using only the numbers you have found in the previous parts of this question, what is the posterior probability that her baby has Down Syndrome? How much larger is this compared to her prior probability?

Sarah Jessica Parker Is 39