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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Comments
I disagree with this answer. The correct answer is 95%. The question is "What percentage of the people WHO TESTED POSITIVE had the disease..." If 5% had false positives.
Then 95% of the people who tested positive would actually have the disease. Then 1 in 1000 is irrelevant.
Then 95% of the people who tested positive would actually have the disease. Then 1 in 1000 is irrelevant.
Okay, I retract my comment above, I misread the teaser.
If 100,000 people are tested, 100 will really have the disease, 99,000 would not. of these 99,900, 4995 would test positive falsely. So 5095 people in 100,000 would test positive.
So 100 in 5095 would actually have the disease in those that tested positive. This is the 1.96% in the answer.
If 100,000 people are tested, 100 will really have the disease, 99,000 would not. of these 99,900, 4995 would test positive falsely. So 5095 people in 100,000 would test positive.
So 100 in 5095 would actually have the disease in those that tested positive. This is the 1.96% in the answer.
Huh? You should reword this.
A few things...
Leftclick, your answer is close but wrong. 100%-.1%=99.9%healthy population. 5% of this healthy population is not 5% of the whole it is only 4.995%. Added to the sick .1%, we get 5.095%. .1/5.095 is 1.9627%
Rerepete's calculation was correct, but did not carry the decimal far enough to prove you wrong.
Also, The only thing we know about the test is that it gives false positives. We don't know if it gives ANY flase negatives or true positives. The question does not state if the sick people will actually be detected. If the test will give a false positive to 4.995% of the population, but does not accurately test positive for ANY of the sick .1%, then the answer is ZERO!
The only person I can agree with completely is FerilMaster97..."You should reword this"
Leftclick, your answer is close but wrong. 100%-.1%=99.9%healthy population. 5% of this healthy population is not 5% of the whole it is only 4.995%. Added to the sick .1%, we get 5.095%. .1/5.095 is 1.9627%
Rerepete's calculation was correct, but did not carry the decimal far enough to prove you wrong.
Also, The only thing we know about the test is that it gives false positives. We don't know if it gives ANY flase negatives or true positives. The question does not state if the sick people will actually be detected. If the test will give a false positive to 4.995% of the population, but does not accurately test positive for ANY of the sick .1%, then the answer is ZERO!
The only person I can agree with completely is FerilMaster97..."You should reword this"
I got the same answer as Spockinasmock...with the same questions regarding the false negatives.
A agree with rerepete's second answer and disagree with FerilMaster97; the question is fine.
The answer is right, but only if there are no false negatives, i.e. 100% of the people who are sick test positive. An interesting challenge would be to add in a percentage of false negatives, say 5% and find what the percentage would be then.
I have to say I stand by my answer on this one.
I agree about the false negatives but you have to assume there are none since it doesn't mention it. Perhaps it should have been explicit about that though.
I agree about the false negatives but you have to assume there are none since it doesn't mention it. Perhaps it should have been explicit about that though.
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