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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?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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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?
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?
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