Question

Estimates of the prevalence of Alzheimer's disease have recently been provided by Pfeffer et al. [8]. The estimates are given in Table $3.5 .$ Suppose an unrelated 77 -year-old man, 76 -year-old woman, and 82-year-old woman are selected from a community.Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both women?

Name: Problem 21, Chapter 3: Fundamentals of Biostatistics
Uploaded: 2024-01-12T11:36:19-08:00
Channel: Shu Naito
Description: Estimates of the prevalence of Alzheimer's disease have recently been provided by Pfeffer et al. [8]. The estimates are given in Table 3.5 . Suppose an unrelated 77 -year-old man, 76 -year-old woman, and 82-year-old woman are selected from a community.Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both women?

   Estimates of the prevalence of Alzheimer's disease have recently been provided by Pfeffer et al. [8]. The estimates are given in Table $3.5 .$ Suppose an unrelated 77 -year-old man, 76 -year-old woman, and 82-year-old woman are selected from a community.Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both women?

Fundamentals of Biostatistics

Bernard Rosner 8th Edition

Chapter 3, Problem 21

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Solved by Expert Shu Naito

01/12/2024

Step 1

We have three individuals: a 77-year-old man, a 76-year-old woman, and an 82-year-old woman. We know that two of these three individuals have Alzheimer's disease. We need to find the conditional probability that both individuals with Alzheimer's are women. Show more…

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Estimates of the prevalence of Alzheimer's disease have recently been provided by Pfeffer et al. [8]. The estimates are given in Table $3.5 .$ Suppose an unrelated 77 -year-old man, 76 -year-old woman, and 82-year-old woman are selected from a community.Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both women?

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Key Concepts

Combinatorial Analysis

This concept involves counting the number of ways events can occur, which is crucial when determining the likelihood of specific outcomes in a given scenario. Here, the method helps in assessing how many favorable combinations (e.g., both affected individuals being women) exist relative to all possible combinations that satisfy the condition that two individuals have Alzheimer’s disease.

Conditional Probability

This concept refers to the probability of an event occurring given that another event has already occurred. In problems like this, the analysis focuses on a reduced sample space that fits the known condition—in this case, that two out of three individuals have Alzheimer’s disease. Understanding conditional probability is essential for correctly updating the chances of intersecting events based on additional information.

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