The probability that a person with certain symptoms has hepatitis is 0.8. The blood test used to confirm this diagnosis gives positive results for 90% of people with the disease and 5% of those without the disease. What is the probability that an individual who has the symptoms and who reacts positively to the test actually has hepatitis? The probability is (Type an integer or decimal rounded to four decimal places as needed.)

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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The probability that a person with certain symptoms has hepatitis is 0.8. The blood test used to confirm this diagnosis
gives positive results for 90% of people with the disease and 5% of those without the disease. What is the probability
that an individual who has the symptoms and who reacts positively to the test actually has hepatitis?
The probability is
(Type an integer or decimal rounded to four decimal
places as needed.)
Transcribed Image Text:The probability that a person with certain symptoms has hepatitis is 0.8. The blood test used to confirm this diagnosis gives positive results for 90% of people with the disease and 5% of those without the disease. What is the probability that an individual who has the symptoms and who reacts positively to the test actually has hepatitis? The probability is (Type an integer or decimal rounded to four decimal places as needed.)
Expert Solution
Step 1

event A : has hepatitis

event+ve : test positive

 

 

P(A) = 0.8

P(A') = 1 -0.8 =0.2

P(+ve|A) = 0.90

P(+ve|A') = 0.05

P(A|+ve) = ? 

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