In pregnancy, women often undergo screening to assess whether their fetus is likely to have Down Syndrome. The screening test evaluates levels of specific hormones in the blood. Screening test results are reported as positive or negative, indicating that a woman is more or less likely to be carrying an affected fetus. Suppose that a population of N=4,810 pregnant women undergo the screening test and are scored as either positive or negative depending on the levels of hormones in the blood. In addition, suppose that each woman is followed to birth to determine whether the fetus was, in fact, affected with Down Syndrome.

The results of the screening tests are summarized below: Using this table, calculate the following: 

a) the probability that a woman with a positive screening test has an affected fetus  

b) the probability that a woman with a negative test has an affected fetus 

c) sensitivity and specificity

d) false positive fraction and false negative fraction

e) positive predicuve value and negative predictive value

Screening Test Positive Negative Total Down Syndrome a 9 10 C No Down Syndrome 351 b 4.449 d 4,800 fu Total 350 4.450 4.810