This is a Statistics problem. Please explain each step thoroughly.  The problem I'm having issues with is shown below: Suppose there is a new test that detects whether people have a disease. If a person has the disease, then the test correctly identifies that person as being sick 99.9 percent of the time (the sensitivity of the test). If a person does not have the disease, then the test correctly identifies the person as being well 97 percent of the time (the specificity of the test). Suppose that 2 percent of the population has the disease. Find the probability that a randomly selected person has the disease given that they test positive for the disease.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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This is a Statistics problem. Please explain each step thoroughly. 

The problem I'm having issues with is shown below:

Suppose there is a new test that detects whether people have a disease. If a person has the disease, then the test correctly identifies that person as being sick 99.9 percent of the time (the sensitivity of the test). If a person does not have the disease, then the test correctly identifies the person as being well 97 percent of the time (the specificity of the test). Suppose that 2 percent of the population has the disease. Find the probability that a randomly selected person has the disease given that they test positive for the disease.

Suppose there is a new test that detects whether people have a disease. If a person has the disease,
then the test correctly identifies that person as being sick 99.9 percent of the time (the sensitivity of the
test). If a person does not have the disease, then the test correctly identifies the person as being well 97
percent of the time (the specificity of the test). Suppose that 2 percent of the population has the disease.
Find the probability that a randomly selected person has the disease given that they test positive for the
disease.
Transcribed Image Text:Suppose there is a new test that detects whether people have a disease. If a person has the disease, then the test correctly identifies that person as being sick 99.9 percent of the time (the sensitivity of the test). If a person does not have the disease, then the test correctly identifies the person as being well 97 percent of the time (the specificity of the test). Suppose that 2 percent of the population has the disease. Find the probability that a randomly selected person has the disease given that they test positive for the disease.
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