bayes' theorem

The probability that a person has a deadly virus is 5 in 1000. A test will correctly diagnose this disease 95% of the time and incorrectly on 20% of occasions.

Find the probability of this test giving correct diagnosis. <-- not sure how to set up this expression.

Quote:

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Originally Posted by shawli

The probability that a person has a deadly virus is 5 in 1000. A test will correctly diagnose this disease 95% of the time and incorrectly on 20% of occasions.

Find the probability of this test giving correct diagnosis. <-- not sure how to set up this expression.

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Pr(correct diagnosis) = Pr(Correct diagnosis | Person has disease) x Pr(Person has disease) + Pr(Correct diagnosis | Person does not have disease) x Pr(Person does not have disease).