4.82 A blood test for hepatitis has the following accuracy:

1 2

a 3

4 b

A 1

2 a

3 B

4 b

Test Result

 

Patient with Hepatitis 0.90 0.10 Patient without Hepatitis 0.01 0.99 The disease rate in the general population is 1 in 10,000.

a What is the probability that a person actually has hepatitis if he or she gets a positive blood test result?

b A patient is sent for a blood test because he has lost his appetite and has jaundice. The physician knows that this type of patient has probability 0.5 of having hepatitis. If this patient gets a positive result on his blood test, what is the probability that he has hepatitis?