Answered: Suppose 0.1% of the population have a…

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

Suppose 0.1% of the population have a new disease. A test is developed for the disease. 98% of people without the disease will receive a negative test result. 99.5% of people with the disease will receive a positive test result. A random person who was tested for the disease is chosen. What is the probability that the chosen person does not have the disease and got a negative test result?

N = negative test results

H = does not have the disease

P(N and H) = P(N|H) x P(H) or 2. P(H|N) x P(N) [use formula 1]

= (0.98) P

Expert Solution

Step 1: Determine the given information

For the defined events, " $N :$ negative test results" and " $H :$ does not have the disease", the following events are interpreted:

$N^{c} :$ positive test results

$H^{c} :$ have the disease

The given probabilities are:

The probability that a selected person has the disease, $P (H^{c}) = 0.1 % = 0.001$ .

The probability that a selected person received a negative test result, provided that the person does not have the disease, i.e., $P (N | H) = 98 % = 0.98$ .