# Question

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• #48613

walden
Participant

You read an article in the newspaper about a disease in North America.  It stated that about 3 persons in a million have this disease.

You were quite concerned and your doctor referred you to take a test that is 95% reliable.  A week later, your doctor phoned you and told you that the test result was positive.
what is the probability that you actually have that disease

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#164518

Dr. Scott
Participant

Chris,
First, if only 3 in a million have this disease I wouldn’t waste my time getting the test. That is, unless I exhibited the symptoms of the disease.
I assume the measure or the test was correctly administered (in the same manner that led to the 95% confidence in the test).
Bottom line is, from a technical point of view, you can never say with certainty that the person does not have the disease (i.e., you cant prove the negative). You can only say there is a 5% chance the positive is wrong.
Hope this helps,
Dr. Scott

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#164520

Brandon
Participant

I took the test – my doctor called and said he had bad news and worse news.
Bad news – I have the disease & 24 hours to live.
Worse news – he meant to call yesterday.

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#164525

Ward
Participant

I literally laughed out loud, but I can’t bring myself to type “LOL”

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#164526

Dr. Scott
Participant

What am I going to do with you? Like Pete though, I had to laugh my parts off with that one.
Thanks for the grin,
Dr. Scott

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#164535

BC
Participant

It’s less than one tenth of one percent.  Is this a homework problem?
Now go apply this concept to acceptance sampling in the plant.

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#164536

Iain Hastings
Participant

This is a conditional probability problem. You know that the probability of testing +ve intersected with the probability that you don’t have the disease is 0.05. By definition this equals the probability that you test +ve times the probability (don’t have disease/Test +ve). You should be able to work it out from there.
Another way to look at it is that out of 1M people 3 will have the disease but 50003 in total will test +ve.
(I assume that when you say 95% reliable you mean that 5% of the time the test shows +ve even if the subject does not have the disease. Another point – this only works if you were taking part in random testing…If your doctor directed you to take the test then you presumably have the symptoms so the probability will be much higher that you have the disease. You may want to suggest that your instructor reword this question in future.)

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#164564

Sloan
Participant

This is a tricky question. I like Dr. Scott’s answer best, that all you can say is that there is a 5% chance the test result was wrong. If you took the test completely at random (You had no symptoms) then you could say that there is a much greater probability of the test giving a false positive than you actually having the disease. Taken completely at random, you have a 1 in 20 chance of seeing a false positive (95% accuracy) while you have only a 1 in 333,333.33 chance of having the disease.

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