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by manhhiep2509 » Fri Sep 26, 2014 7:38 am
The probability of having a particular disease in a population is 5%. A diagnostic test to determine if a person has this disease is 83% accurate. Find the probability that a randomly selected person tests positive.

Do you think 83% is the probability to choose a person that has positive diagnose and has the disease, or is the probability a person has disease if he is chosen from a group of people who has positive diagnose?
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by [email protected] » Fri Sep 26, 2014 10:45 am
Hi manhiep2509,

What is the source of this question? I ask because this looks like more of a Statistics question than a GMAT question (where are the 5 answer choices?). If you're studying for the GMAT, then this prompt is not something that you're likely to see on Test Day.

We're not given a lot of information to work with, but here's how the math "works" in this question:

If we have 100 people, then 5 of them have the disease and 95 don't. The test to detect the disease is 83% accurate IF you have the disease. We don't know what happens if you take the test but don't have the disease, so I have to assume that it's 100% accurate in THAT situation.

5(.83) = 4.15

4.15/100 = 4.15%

This would represent the probability of randomly selecting a person who has the disease AND the test successfully confirming it.

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