A new test has been devised for detecting a particular type of cancer. If
the test is applied to a person who has this type of cancer, the probability
that the person will have a positive reaction is 0.95 and the probability
that the person will have a negative reaction is 0.05. If the test is applied
to a person who does not have this type of cancer, the probability that the
person will have a positive reaction is 0.05 and the probability that the
person will have a negative reaction is 0.95. Suppose that in the general
population, one person out of every 100,000 people has this type of cancer.
If a person selected at random has a positive reaction to the test, what is
the probability that he has this type of cancer?

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