There is a test that can be performed on a pregnant women to determine if the fetus has the genetic condition known as Trisomy 21, which causes Down Syndrome. The test performs well: for fetuses with...

There is a test that can be performed on a pregnant women to determine if the fetus has the genetic condition known as Trisomy 21, which causes Down Syndrome. The test performs well: for fetuses with Trisomy 21, the test is positive with probability 0.9914, and for fetuses without Trisomy 21, the test is only positive with probability 0.0006. Assume that the probability
of a fetus carrying Trisomy 21 is 0.001. What are the following quantities?
a. P(Positive Test|Fetus has T21)
b. P(Positive Test|Fetus does not have T21)
c. P(Fetus does not have T21)
d. P(Fetus has T21|Positive Test)
If a woman receives a positive test result for Trisomy 21, what is the probability that her fetus has Trisomy 21?