Question

Ninety-eight percent of all babies survive delivery. However, 15 percent of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 96 percent of the time. If a randomly chosen pregnant woman does not have a $\mathrm{C}$ section, what is the probability that her baby survives?

Name: Problem 12, Chapter 3: A First Course in Probability
Uploaded: 2022-01-17T03:18:29-08:00
Duration: 3 min 44 s
Channel: Wendi Zhao
Description: Ninety-eight percent of all babies survive delivery. However, 15 percent of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 96 percent of the time. If a randomly chosen pregnant woman does not have a C section, what is the probability that her baby survives?

   Ninety-eight percent of all babies survive delivery. However, 15 percent of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 96 percent of the time. If a randomly chosen pregnant woman does not have a $\mathrm{C}$ section, what is the probability that her baby survives?

A First Course in Probability

Sheldon M. Ross 5th Edition

Chapter 3, Problem 12

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Solved by Expert Wendi Zhao

01/17/2022

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98, the probability that a baby has a C section (C) is 0.15, and the conditional probability that a baby survives given that he or she has a C section is 0.96. We want to find the conditional probability that a baby survives given that he or she does not have a C Show more…

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Ninety-eight percent of all babies survive delivery. However, 15 percent of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 96 percent of the time. If a randomly chosen pregnant woman does not have a $\mathrm{C}$ section, what is the probability that her baby survives?

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Key Concepts

Law of Total Probability

This principle allows one to compute the overall probability of an event by breaking it down into several mutually exclusive cases. When the overall outcome can arise from different scenarios, the probabilities are calculated by weighting each conditional probability by the likelihood of its corresponding scenario and then summing these products.

Conditional Probability

Conditional probability is the measure of the likelihood of an event occurring given that another event has already occurred. It is essential for understanding scenarios where the probability of an outcome depends on a specific condition or event being met.

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