how do you form the probability tree for this??
The commonly used test to assess Down's syndrome risk in the unborn foetus is the 'triple test', which combines maternal age with other markers of foetal and maternal health from a single blood test. The test has a 65% detection rate, and a 5% false positive rate. Incidence of Down's syndrome in births from 35 yr old mothers is 1 in 250. The triple test from one 35 yr old mother returns a positive result. What is the probability that her foetus has Down's syndrome?
Out of a random sample of 35 year old mothers:
Probability of false positive = (249/250)*0.05 = 0.0498
Probability of correct positive = (1/250)*0.65 = 0.0026
Probability of false negative (undetected Down's) = (1/250)*0.35 = 0.0014
Probability of correct negative = (249/250)*0.95 = 0.9462
For the woman in question, she is either a false positive or a correct positive.
Probability of Down's = (.0026)/(.0026+.0498) = 0.04962
That equals a probability of 1 in 20.2