A common blood test performed on pregnant women to screen fo

A common blood test performed on pregnant women to screen for chromosome abnormalities in the fetus measures the human chorionic gonadotropin (hCG) hormone. Suppose that in a given population, 2% of fetuses have a chromosome abnormality. The test correctly produces a positive result for a fetus with a chromosome abnormality 92% of the time and correctly produces a negative result for a normal fetus 85% of the time. What proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality? (4pt)

Solution

P(true positive) = P(test positive and actual positive) / P(test positive)

As

P(test positive and actual positive) = P(actual positive) P(test positive|actual positive) = (0.02)(0.92) = 0.0184

P(test positive) = P(actual positive) P(test positive|actual positive) + P(actual negative) P(test positive|actual negative) = (0.02)(0.92) + (1-0.02)(1-0.85) = 0.1654

Then

P(true positive) = P(test positive and actual positive) / P(test positive)

= 0.0184/0.1654

= 0.111245466 [ANSWER]