In Review Exercise 6, suppose we do not know the probability that a newborn weighs less than 2500 grams when the payment source is Medicaid. However, we do know the probability that a newborn weighs less than 2500 grams given their gestational age is less than 37 weeks is 0.

448, and the probability that a newborn weighs less than 2500 grams given their gestational age is greater than or equal to 37 weeks is 0.

041. We also know the probability that an infant's gestational age is less than 37 weeks is 0.

131 [136]. Let A be the event that an infant's gestational age is less than 37 weeks, A the event that their gestational age is greater than or equal to 37 weeks, and B the event that the newborn's birth weight is less than 2500 grams.

(a) What is the probability that a newborn's gestational age is greater than or equal to 37 weeks?

(b) Calculate P(AIB) and P(A2 n B).

(c) Using the total probability rule, calculate P(B). Does this match the probability given in Exercise 6?