Obstetrics
Suppose that infants are classified as low birthweight if they have a birthweight <2,500 g and as normal birthweight if they have a birthweight >2,500 g. Suppose that infants are also classified by length of gestation in the following five categories: <28 weeks, 28-31 weeks, 32-35 weeks, 36 weeks, and 37 weeks. Assume the probabilities of the different periods of gestation are as given in the table below.
Length of gestation Probability
<28 weeks 0.006
28-31 weeks 0.010
32-35 weeks 0.049
36 weeks 0.035
37 weeks 0.900
The following conditional probabilities are given: assume that the probability of low birthweight is 0.948 given a gestation of <28 weeks, 0.700 given a gestation of 28-31 weeks, 0.432 given a gestation of 32-35 weeks, 0.202 given a gestation of 36 weeks, and 0.028 given a gestation of 37 weeks.
(a) What is the probability of having a low birthweight infant? (Round your answer to four decimal places. Hint: Use the Law of Total Probability.)