Acertain genetic condition affects 8% of the population in a city of 10,000. suppose there is a test for the condition that has an error rate of 1% (i. e., 1% false negatives and 1% false positives).

consider the values that would complete the table below.

has condition does not have condition totals

test positive

test negative

totals

what is the probability (as a percentage) that a person has the condition if he or she tests positive? (round your answer to one decimal place.)

Let be the event that a randomly selected person has the condition, and the event that the test returns a positive result. We are given that

(false positive; that is, the event that the test incorrectly returns a positive result)

(false negative; incorrectly returns a negative result)

We want to find . By definition of conditional probability,

By the same definition,

and by the law of total probability,

So we have (and this is known as Bayes' rule)

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