MathDB

Suppose that one of every

500

people in a certain population has a particular disease, which displays no symptoms. A blood test is available for screening for this disease. For a person who has this disease, the test always turns out positive. For a person who does not have the disease, however, there is a

2\%

false positive rate; in other words, for such people,

98\%

of the time the test will turn out negative, but

2\%

of the time the test will turn out positive and will incorrectly indicate that the person has the disease. Let

p

be the probability that a person who is chosen at random from the population and gets a positive test result actually has the disease. Which of the following is closest to

p

<span class='latex-bold'>(A)</span>\ \frac{1}{98}\qquad<span class='latex-bold'>(B)</span>\ \frac{1}{9}\qquad<span class='latex-bold'>(C)</span>\ \frac{1}{11}\qquad<span class='latex-bold'>(D)</span>\ \frac{49}{99}\qquad<span class='latex-bold'>(E)</span>\ \frac{98}{99}

Problem Statement