Consider a prenatal blood test with the following characteristics:

Context: Noninvasive prenatal testing technology, or NIPT, which works well for detecting relatively common conditions like Down syndrome performs much worse when it looks for less common conditions.

To evaluate the validity of this claim, consider a prenatal blood test with the following characteristics:

if the fetus has the disorder, the test comes back positive for sure; if the fetus does not have the disorder, the test comes back positive with probability 0.1%.

Questions:

(a) Suppose one uses this technology to screen for Down syndrome. Assuming Down syndrome has a prevalence of roughly 1 in 200 births, if the test comes back positive, what is the probability that it is a false positive? (b) Suppose, instead, that one uses the above test to screen for DiGeorge syndrome, which, according to the article, has a prevalence of 1 in 4,000 births. If the test comes back positive, what is the probability that it is a false positive? (c) Briefly comment (agree/disagree) on the claim that tests that work relatively well for a fairly common conditions can be much less useful for rarer conditions.