Unformatted text preview: C ⊂ Ω. Note that this is a conditional version of the total probability theorem (conditioned on the event B in this case). Breaking event B up like this into the disjoint partition B ∩ C and B ∩ C c can sometimes be useful in calculating P ( A  B ). 3. (Example 1.18, page 33 of the text.) A test for a certain rare disease is assumed to be correct 95% of the time: if a person has the disease, the test results are positive with probability 0.95, and if the person does not have the disease, the test results are negative with probability 0.95. A random person drawn from a certain population has probability 0.001 of having the disease. Given that the person just tested positive, what is the probability of having the disease? Explain this result intuitively. Page 1 of 1...
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 Spring '11
 Proasin
 Computer Science, Electrical Engineering, Conditional Probability, Probability, Probability theory, total probability theorem

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