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ProbabilityQ&A Library. Initial diagnosis of a patient’s illness was potentially flu (F), cold (C), or hay fever (H), with probabilities 0.1, 0.2, and 0.7 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 (-):•P(+|F) = 0.7P(0|F) = 0.2P(-|F) = 0.1•P(+|C) = 0.1P(0|C) = 0.8P(-|C) = 0.1•P(+|H) = 0.1P(0|H) = 0.2P(-|H) = 0.7•Use the Bayes Theorem to estimate the respective probabilities of F, C, and H given that a +, 0, or – test result has been observed.Question

Asked Jan 31, 2019

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. Initial diagnosis of a patient’s illness was potentially flu (F), cold (C), or hay fever (H), with probabilities 0.1, 0.2, and 0.7 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 (-):•P(+|F) = 0.7P(0|F) = 0.2P(-|F) = 0.1•P(+|C) = 0.1P(0|C) = 0.8P(-|C) = 0.1•P(+|H) = 0.1P(0|H) = 0.2P(-|H) = 0.7•Use the Bayes Theorem to estimate the respective probabilities of F, C, and H given that a +, 0, or – test result has been observed.

Step 1

For bayes' theorem, its always better to draw probabilities in tree diagram to visually analyse them.

Step 2

The probability of F given + is:

Step 3

The probability of F...

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