Lisa is 35 and pregnant for the first time. As a "mature" mother, she is worried about the possibility of having a baby with Down Syndrome. Chances of a 35-year old mother having a baby with Down Syndrome is 1 in 300. Just to be on the safe side, Lisa 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%. Lisa's blood serum test provides a positive result for Down Syndrome. The posterior probability that Lisa's child will have Down Syndrome is:
A) 0.037 or 3.7%.
B) 0.003 or 0.3%.
C) 0.03 or 3%.
D) 0.9 or 90%.

Question

Quizplus · Accepted Answer

To calculate the posterior probability that Lisa's child will have Down Syndrome given a positive test result, we can use Bayes' Theorem. The probability of having a baby with Down Syndrome at age 35 is 1 in 300, or 0.0033. The probability of a positive test if the baby has Down Syndrome is 0.9, and the probability of a positive test if the baby does not have Down Syndrome (false positive rate) is 0.07.Bayes' Theorem formula in this context is: P(DS|Positive) = [P(Positive|DS) * P(DS)] / [P(Positive|DS) * P(DS) + P(Positive|No DS) * P(No DS)]Plugging in the numbers: P(DS|Positive) = (0.9 * 0.0033) / (0.9 * 0.0033 + 0.07 * 0.9967) ≈ 0.037 or 3.7%.This calculation shows that even after a positive test result, the probability that Lisa's child actually has Down Syndrome is about 3.7%.

Lisa Is 35 and Pregnant for the First Time