A widely used blood test for a certain severe medical condit

A widely used blood test for a certain severe medical condition has about a 4.2% rate of false positive results. That is, about 4.2% of people who do not have the disease will still have a positive test! On average, your medical clinic administers this test to about 7 people each week. What is the likelihood of finding at least one false positive in the result? In other words, what is the likelihood that at least 1 person in that will be told incorrectly(!) that they have the disease?

Solution

Let X be the no of persons with false positive result

X is binomial with p = 0.042 and n =7

P(X>=1) = 0.2594

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