{"status": "success", "data": {"description_md": "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 this population and gets a positive test result actually has the disease. Which of the following is closest to $p$?\n\n$\\textbf{(A)}\\ \\frac{1}{98}\\qquad\\textbf{(B)}\\ \\frac{1}{9}\\qquad\\textbf{(C)}\\ \\frac{1}{11}\\qquad\\textbf{(D)}\\ \\frac{49}{99}\\qquad\\textbf{(E)}\\ \\frac{98}{99}$", "description_html": "

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 this population and gets a positive test result actually has the disease. Which of the following is closest to p ?

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\\textbf{(A)}\\ \\frac{1}{98}\\qquad\\textbf{(B)}\\ \\frac{1}{9}\\qquad\\textbf{(C)}\\ \\frac{1}{11}\\qquad\\textbf{(D)}\\ \\frac{49}{99}\\qquad\\textbf{(E)}\\ \\frac{98}{99}

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2012 AMC 10B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc10B_p19", "prev": "/problem/12_amc10B_p17"}}