1. We are interested in two events. First event is whether a baby is born via a

Question

1. We are interested in two events. First event is whether a baby is born via a Cesarean section (C for Cesarean and C c for not). The other event is whether the baby survived the delivery process (S for survive and S c for not survive). Given a C section is performed, the baby survives 96% of the time. Given a C section is not performed, the baby survives 98% of the time. In the U.S. there is a 15% chance of a birth involves Cesarean (C) section.

a. What is the probability that a randomly chosen mother has a C section and her baby survives?

b. What is the probability that a randomly chosen baby survives birth?

c. Given a baby does survive birth, what is the probability the mother had a C section?

Explanation / Answer

here probability of  Cesarean section =P(C)=0.15

and probability of bot Cesarean section=P(Cc)=1-0.15=0.85

P(S|C)=0.96 and P(S|Cc)=0.98

a)  probability that a randomly chosen mother has a C section and her baby survives =P(C nS)=P(C)*P(S|C)

=0.15*0.96=0.144

b)probability that a randomly chosen baby survives birth=P(S)=P(C)*P(S|C)+P(Cc)*P(S|Cc)

=0.15*0.96+0.85*0.98=0.977

c) probability the mother had a C section; Given a baby does survive birth=P(C|S)=P(C)*P(S|C)/P(S)

=0.15*0.96/0.977=0.1474

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