A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 8% of the time if the person does not have the virus. (This 8% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A|B)- b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A'|B') =

A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 8% of the time if the person does not have the virus. (This 8% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A|B)- b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A'|B') =

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Description: M0/1A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% ofthe time if the person has the virus and 8% of the time if the person does not have the virus. (This 8% resultis called a false positi

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Question

M0/1
A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of
the time if the person has the virus and 8% of the time if the person does not have the virus. (This 8% result
is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests
positive".
a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B).
Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A|B)=
b) Find the probability that a person does not have the virus given that they test negative, i.e. find
P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A'|B') =
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Expert Solution

Step 1

Let's draw tree diagram from given information ,

A : Event that the person is infected

P( A ) = 1/400 = 0.0025

B : Event that the person tests is positive.

we have ,

P( A ) = 0.0025 , P( A') = 0.9975

P( B | A ) = 0.9 , P( B' | A ) = 0.1

P( B | A' ) = 0.08 , P( B' | A' ) = 0.92

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