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After a meningitis outbreak in a hospital, a doctor estimates there is a 20% chance that any given patient has meningitis. Each patient is tested using the above test. For patient A, the test comes out positive. What is the chance that patient A has meningitis?
A new medical test for meningitis is evaluated on 500 patients, 50 of whom are known to have meningitis and 450 of whom are known not to have meningitis. The results are shown in the table
Table: Positive + known: 47 Positive + Not-known: 13 Negative + known: 3 Negative + Not-known: 437
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