**Understanding Disease Testing Probabilities**A laboratory test for detecting a specific disease produces certain results based on different scenarios. Here are the probabilities associated with the test results:- The test shows a positive result for 5% of people who do not have the disease (false positive rate).- The test shows a negative result for 0.3% of people who have the disease (false negative rate).- Studies indicate that this disease affects approximately 2% of the population.### Problems to Solve:**a. Probability of Testing Positive**Determine the probability that a randomly selected person would test positive for this disease. Formulate and demonstrate your approach.**b. Probability of a False Positive**Calculate the probability that a person who tests positive actually does not have the disease. Provide a detailed explanation of your method.

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Description: **Understanding Disease Testing Probabilities**A laboratory test for detecting a specific disease produces certain results based on different scenarios. Here are the probabilities associated with the test results:- The test shows a positive result f

15. a. The detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease. That is, Ppositive results | do not have disease=0.05, the test gives a negative result 0.3 percent of the time for people who have the disease, then test gives a positive result 99.7 percent of the time for people who have the disease. That is, Ppositive results | have disease=0.997, and the large scale studies have shown that the disease occurs in about 2 percent of the population. That is, Phave disease=0.02,Pdo not have disease=0.98. The probability that a person selected at random would test positive for this disease is, PPositive results=Ppositive results ∩ have disease+Ppositive results ∩ do not have disease=P have diseasePpositive results | have disease+Pdo not have diseasePpositive results | do not have disease=0.02×0.997+0.98×0.05=0.06894 Thus, the probability that a person selected at random would test positive for this disease is 0.06894.b. The probability that a person selected at random who test positive for the disease does not have the disease is, Pdo not have disease | positive results=Pdo not have disease ∩ positive resultsPpositive results=Pdo not have diseasePpositive results | do not have diseasePpositive results=0.98×0.050.06894=0.0490.06894=0.7108 Thus, the probability that a person selected at random who test positive for the disease does not have the disease is 0.7108.

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Statistics

15. A laboratory test for the detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease. The test gives a negative result 0.3 percent of the time for people who have the disease. Large-scale studies have shown that the disease occurs in about 2 percent of the population. a. What is the probability that a person selected at random would test positive for this disease? Show your work. b. What is the probability that a person selected at random who tests positive for the disease does not have the disease? Show your work.

15. A laboratory test for the detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease. The test gives a negative result 0.3 percent of the time for people who have the disease. Large-scale studies have shown that the disease occurs in about 2 percent of the population. a. What is the probability that a person selected at random would test positive for this disease? Show your work. b. What is the probability that a person selected at random who tests positive for the disease does not have the disease? Show your work.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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