Initial diagnosis of a patient's illness was potentially flu (F), cold (C), or hay fever (H), with probabilities 0.1, 0.3, and 0.6 respectively. A lab test was then taken from the patient. Past tests on similar patients show the following conditional probabilities on the test result being positive (+), neutral (0), or negative (-):

Use the Bayes Theorem to estimate the respective probabilities of F, C, and H given that a +, 0, or - test result has been observed.

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P (+F) = 0.8 P (0|F) = 0.1 P (-|F) = 0.1 P (-|C) = 0.1 Р (НС) - 0.2 Р(0C) — 0.7 Р (-Н) — 0.6 P (+H) = 0.1 Р (ОН) — 0.3