It is known that a rare disease, K, is present only in 0.2% of the population. Performance of the test by a physician's diagnostic test for the presence or absence of the disease K is given in Table, where R+ denotes the positive test result, and R- denotes the negative result. Also, Kc denotes absence of the disease.
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Table
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R+
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R-
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K
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0.98
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0.02
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Kc
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0.01
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0.99
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(a) What is the probability that a patient has the disease, if the test result is positive?
(b) What is the probability that a patient has the disease, if the test result is negative?