Lisa is 40 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 40-year old mother having a baby with Down Syndrome is 1 in 100. 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 86% of the time. There is, however, a small "false positive" rate of 5%. 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) 86%.
B) 1%.
C) 5%.
D) 14.8

Question

Quizplus · Accepted Answer

The posterior probability is calculated using Bayes' theorem. Given a positive test result, the probability that Lisa's child actually has Down Syndrome is found by dividing the probability of a true positive (the probability of having Down Syndrome times the sensitivity of the test) by the sum of the probability of a true positive and the probability of a false positive (the probability of not having Down Syndrome times the false positive rate). This calculation yields approximately 14.8%.

Lisa Is 40 and Pregnant for the First Time