Answered: A certain disease affects 1% of the…

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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Question

A certain disease affects 1% of the population. A diagnostic test for the disease is 99% accurate (i.e. the test will correctly identify 99% of infected individuals and 99% of uninfected individuals). Given that a randomly selected person tests positive, what is the probability that they actually have the disease?

Expert Solution

Step 1

Introduction

Bayes' theorem is a mathematical formula used in statistics to calculate the probability of an event based on prior knowledge. It provides a way to revise probabilities when new evidence becomes available. The theorem states that the probability of an event (A) given the occurrence of another event (B) is equal to the probability of event (B) given event (A) times the prior probability of event (A) divided by the marginal probability of event (B). In this question, we will use Bayes' theorem to calculate the probability of a person having a disease given a positive test result, taking into account the accuracy of the test and the prevalence of the disease in the population.