Linda is 22 and pregnant for the first time. Chances of a 22-year old mother having a baby with Down Syndrome is 1 in 1000. Just to be on the safe side, Linda 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%. Linda's blood serum test provides a positive result for Down Syndrome. The probability that Linda's child will have Down Syndrome is (approximately):
A) 86%.
B) 1.7%.
C) 0.1%.
D) 63%.

Question

Quizplus · Accepted Answer

This is a classic example of applying Bayes' theorem. The probability of having a baby with Down Syndrome at Linda's age is 1 in 1000 (0.1%), and the test has a true positive rate of 86% and a false positive rate of 5%. The probability that Linda's child actually has Down Syndrome given a positive test result can be calculated using Bayes' theorem. The calculation shows that the probability is significantly lower than the test's true positive rate, leading to an approximate probability of 1.7%.

Linda Is 22 and Pregnant for the First Time