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?
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?
A First Course in Probability (10th Edition)
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![**Question 8**
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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 be classified as abused? [ ]
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Transcribed Image Text:**Question 8**
**Details:**
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 be classified as abused? [ ]
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[ ]
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where is the rest all i still need ans for e and f.
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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?
Add any comments below.
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