Using the Multiplication Rule In Exercises 19-32, use the Mult...

Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

29. In Vitro Fertilization In a recent year, about 1.9% of all infants born in the U.S. were conceived through assisted reproductive technology (ART). Of the ART deliveries, about 26.4% resulted in multiple births. (Source: Morbidity and Mortality Weekly Report)

a. Find the probability that a randomly selected infant was conceived through ART and was part of a multiple birth.

Accepted Answer

All right, hello, everyone. So this question says, a recent study found that 2.5% of all newborns in the country were delivered by cesarean section due to medical emergencies. Among these emergency cesarean deliveries, 18.7% involved premature births. What is the probability that a randomly chosen newborn was delivered by emergency cesarean section? Or emergency cesarean section, excuse me, and was also premature. So this question Defines two events. Let's say that E, for example, is the event that the newborn was delivered by the emergency C-section. And then we also have the probability or the event P, which is that the newborn was born premature. So, in this case, according to the information that we are given, the probability that the newborn was delivered by emergency C-section, that is, the probability of E, is equal to 0.025. That's that 2.5%. So we're also given. The probability of P given E. That is the probability that a newborn was born premature, given that. The newborn was born via emergency C-section is equal to 0.187. So to find the probability. That a chosen newborn was delivered by emergency C-section and was also premature corresponds to the probability of E intersection P. Which we can solve for using the multiplication rule. So in this case, the probability of E intersection P is equal to the probability of E multiplied by the probability of P given E. So here that's. 0.025, multiplied by 0.187. Which gives you 0.004675. And therefore Your final answer, that is the probability that a randomly chosen newborn was delivered via emergency C-section and was also premature. Is 0.004675. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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Key Concepts

Multiplication Rule

Conditional Probability

Joint Probability

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