Math Problem Statement
A certain virus infects one in every 200 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 a percent rounded to the nearest fourth decimal place 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 as a percent rounded to the nearest fourth decimal place and do not include a percent sign. P(Ā|B̄) = %
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Conditional Probability
Bayes' Theorem
Law of Total Probability
Formulas
Bayes' Theorem: P(A|B) = [P(B|A) * P(A)] / P(B)
Law of Total Probability: P(B) = P(B|A) * P(A) + P(B|A') * P(A')
Theorems
Bayes' Theorem
Law of Total Probability
Suitable Grade Level
Grades 11-12
Related Recommendation
Calculating Probability Using Bayes' Theorem for Disease Testing
Conditional Probability with Bayes' Theorem: Virus Detection Example
Calculating Conditional Probability of Virus Infection with Bayes' Theorem
Bayes' Theorem for Medical Test: Calculating Disease Probability with False Positives and Negatives
Bayes' Theorem: Probability of Cancer Given a Positive Test Result