Find the probability that a person has a virus given that they have tested positive,I.e P(A/B) round answer to the nearest tenth of a percent B. Find the probability that a person does not have the virus given that they test negative.
Find the probability that a person has a virus given that they have tested positive,I.e P(A/B) round answer to the nearest tenth of a percent B. Find the probability that a person does not have the virus given that they test negative.
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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Question
A certain virus infects 1 in every 400. A test used to detect the virus in a person is positive 85% 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
A. Find the probability that a person has a virus given that they have tested positive,I.e P(A/B)
round answer to the nearest tenth of a percent
B. Find the probability that a person does not have the virus given that they test negative. I.E, find (A/B) round to the nearest tenth of a percent
![### Understanding Probability in Medical Testing
**Scenario Description:**
A certain virus infects one in every 400 people. A test used to detect the virus returns a positive result 85% 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 tests positive."
**Questions:**
a) *Find the probability that a person has the virus given that they tested positive, denoted as \( P(A \mid B) \). Round your answer to the nearest tenth of a percent.*
\[ P(A \mid B) = \_\_\_\% \]
b) *Find the probability that a person does not have the virus given that they tested negative, denoted as \( P(A' \mid B') \). Round your answer to the nearest tenth of a percent.*
\[ P(A' \mid B') = \_\_\_\% \]
**Explanation:**
These questions involve using conditional probability and Bayes’ theorem to calculate the probabilities based on the provided data.
1. *P(A | B)* refers to the probability that someone actually has the virus given that they tested positive.
2. *P(A' | B')* refers to the probability that someone does not have the virus given that they tested negative.
Understanding and solving these problems involve applying principles of probability, particularly focusing on how test sensitivity and specificity affect the interpretation of test results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3911c819-e187-49b9-9fcc-b89884a563f1%2Fe76fc033-6a4c-42b8-bb18-74e711429654%2F4cznrlf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Probability in Medical Testing
**Scenario Description:**
A certain virus infects one in every 400 people. A test used to detect the virus returns a positive result 85% 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 tests positive."
**Questions:**
a) *Find the probability that a person has the virus given that they tested positive, denoted as \( P(A \mid B) \). Round your answer to the nearest tenth of a percent.*
\[ P(A \mid B) = \_\_\_\% \]
b) *Find the probability that a person does not have the virus given that they tested negative, denoted as \( P(A' \mid B') \). Round your answer to the nearest tenth of a percent.*
\[ P(A' \mid B') = \_\_\_\% \]
**Explanation:**
These questions involve using conditional probability and Bayes’ theorem to calculate the probabilities based on the provided data.
1. *P(A | B)* refers to the probability that someone actually has the virus given that they tested positive.
2. *P(A' | B')* refers to the probability that someone does not have the virus given that they tested negative.
Understanding and solving these problems involve applying principles of probability, particularly focusing on how test sensitivity and specificity affect the interpretation of test results.
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