The probability that a person with certain symptoms has hepatitis is 0.70.7. The blood test used to confirm this diagnosis gives positive results for 9292% of people with the disease and 55% 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?

Therefore the probability that an individual who has the symptoms and reacts positively to test actually positively is 0.98.

Step-by-step explanation:

Bayes' Theorem:

A,B = events

P(A|B)= probability of A given B is true

P(A),P(B)= the independent probabilities of A and B.

In this case we use Bayes' Theorem  (spacial case)

F= a person with symptoms has hepatitis

F'=  a person with symptoms does have not hepatitis

E= Blood test positive.

P(F)= 0.7

P(F') = 1- 0.7 = 0.3

P(E|F)= 92% = 0.92

P(E|F')= 5%=0.05

            ≈0.98

Therefore the probability that an individual who has the symptoms and reacts positively to test actually positively is 0.98.

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