a. What is the probability that the selected child is abused? b. What is the probability that the selected child is abused and is classified as abused? c. What is the probability that the selected child is classified as abused?
a. What is the probability that the selected child is abused? b. What is the probability that the selected child is abused and is classified as abused? c. What is the probability that the selected child is classified as abused?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
Related questions
Question
![What proportion of children in a certain population are abused? The classification of whether a child is abused is determined by a social worker. But social workers
are not perfect, and diagnoses are sometimes incorrect. Suppose if a child is abused (A), then a social worker will classify that child as abused with probability
0.97 and as non-abused with probability 0.03. If the child is non-abused then the social worker classifies the child as non-abused with probability 0.96 and as
abused with probability 0.04. Based upon many examinations it is known that about 1.3% of children in the population are abused. Suppose 1.3% of the
population actually is abused. We randomly select one child from the population to be examined by a social worker to detect for abuse
a. What is the probability that the selected child is abused?
b. What is the probability that the selected child is abused and is classified as abused?
c. What is the probability that the selected child is classified as abused?
d. What is the probability that the selected child is classified as non-abused?
e. What is the probability that the selected child is abused given that the child is classified as abused?
f. If 1000 random children from the (large) population are examined, about how many would classified as abused?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43a4cf3b-7b0c-4ef2-a9bb-2a52eee0ff0c%2F68ebbc76-2fc9-47b8-a484-b58f8cfd231c%2Fswbi3xh_processed.png&w=3840&q=75)
Transcribed Image Text:What proportion of children in a certain population are abused? The classification of whether a child is abused is determined by a social worker. But social workers
are not perfect, and diagnoses are sometimes incorrect. Suppose if a child is abused (A), then a social worker will classify that child as abused with probability
0.97 and as non-abused with probability 0.03. If the child is non-abused then the social worker classifies the child as non-abused with probability 0.96 and as
abused with probability 0.04. Based upon many examinations it is known that about 1.3% of children in the population are abused. Suppose 1.3% of the
population actually is abused. We randomly select one child from the population to be examined by a social worker to detect for abuse
a. What is the probability that the selected child is abused?
b. What is the probability that the selected child is abused and is classified as abused?
c. What is the probability that the selected child is classified as abused?
d. What is the probability that the selected child is classified as non-abused?
e. What is the probability that the selected child is abused given that the child is classified as abused?
f. If 1000 random children from the (large) population are examined, about how many would classified as abused?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,