Solution Found!
Refer to Example 2.26. Assume that the proportion of people in the community who have
Chapter 2, Problem 30(choose chapter or problem)
Refer to Example 2.26. Assume that the proportion of people in the community who have the disease is 0.05.
a. Given that the test is positive, what is the probability that the person has the disease?
b. Given that the test is negative, what is the probability that the person does not have the disease?
Questions & Answers
QUESTION:
Refer to Example 2.26. Assume that the proportion of people in the community who have the disease is 0.05.
a. Given that the test is positive, what is the probability that the person has the disease?
b. Given that the test is negative, what is the probability that the person does not have the disease?
ANSWER:
Step 1 of 3
Given that,
Assume that the proportion of people in the community who have the disease is 0.05.
Also,
Example 2.26 provides the following information:
If a person has the disease, the probability that the test will produce a positive signal is 0.99. If a person does not have the disease, the probability that the test will produce a positive signal is 0.01.
Let:
D = Event that the person actually has the disease
TP = Event that the test results positive
TN = Even that the test results negative
So,
The provided information can be written as:
