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A test indicates the presence of a particular disease 90%
Chapter 1, Problem 12E(choose chapter or problem)
PROBLEM 12E
A test indicates the presence of a particular disease 90% of the time when the disease is present and the presence of the disease 2% of the time when the disease is not present. If 0.5% of the population has the disease, calculate the conditional probability that a person selected at random has the disease if the test indicates the presence of the disease.
Questions & Answers
QUESTION:
PROBLEM 12E
A test indicates the presence of a particular disease 90% of the time when the disease is present and the presence of the disease 2% of the time when the disease is not present. If 0.5% of the population has the disease, calculate the conditional probability that a person selected at random has the disease if the test indicates the presence of the disease.
ANSWER:
Answer :
Step 1 of 2 :
Given,
A test indicates the presence of a particular disease 90% of the time when the disease is present and the present and the presence of the disease 2% of the time when the disease is not present.
The claim is to find the conditional probability that a person selected at random has the disease if the test indicates the presence of the disease, when 0.5% of the population has the disease.
The probability that the selected person has disease = P(A)
= 0.5%
= 0.005
The probability that the selected person does not have disease = P(B)
= 1 - P(A)
= 1 - 0.005
= 0.995.
Let, P(C) be the test indicates the disease
P(C/A) = 90%
= 0.90
P(C/B) = 2%
= 0.02