Brain Teasers
The Medical Test
A medical test is being administered to people to screen for a particular disease. What percentage of the people who test positive would actually have the disease, if the disease is present in 1 person in 1000 and the test gives a positive result for 5% of people who do not actually have the disease?
Answer
1 person in 51, or around 1.96% of those who test positive, would actually have the disease.The disease is present in 0.1% of cases, and the test gives a false positive 5% of the time, for a total of 5.1% positive results. Of these, only 0.1% actually have the disease, for a ratio of 0.1% / 5.1% = 1/51 or approximately 1.960784%
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