1. A diagnostic test has
a probability 0.95 of giving a positive result when applied to a
person suffering from a certain disease, and a probability 0.10 of
giving a (false) positive when applied to a non-sufferer. It is
estimated that 0.5 % of the population are sufferers. Suppose that
the test is now administered to a person about whom we have no
relevant information relating to the disease (apart from the fact
that he/she comes from this population). Calculate the following
probabilities:
a) that the test result will be
positive;
b) that, given a positive result, the
person is a sufferer;
c) that, given a negative result, the
person is a non-sufferer;
d) that the person will be misclassified
(misdiagnosed).
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