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 workersare 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 probability0.97 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 asabused 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 thepopulation actually is abused. We randomly select one child from the population to be examined by a social worker to detect for abusea. 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?

Let us define some events A : a child is abused B : a child is not abused. E : a child is…

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

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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?

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