How likely are you to have the disease?

Well, without giving this much thought, I would think 99%. But, clearly, I'm suppose to give it thought, so...

0.01% (1 in 10,000) of the time someone will have the disease. This seems like the tricky bit (you even wrote it without using numerals which seems sneaky and thus makes me assume it's very important).

99% of the time the test gives an accurate result.
Perhaps, it's better to say it as 1% of the time the test gives an inaccurate result.

So... that means the test more often gives a false-positive than a false-negative (because, the chance of someone having the disease is actually very small). So, perhaps, I don't have that much to worry about. Now, lets see if I can come up with my actual chances...

Out of 10,000 people, 1 will have the disease. If each of those 10,000 people takes the test, 1% will get an inaccurate result. Thus, 100 of them will get an inaccurate result. Since only 1 should have the disease, that inaccurate result would usually be a false-positive. So, I'm one of the 100, but only 1 of the 100 (there's even a 1% chance it's not one of the 100) has it. So, I'd say I'm close to a 1% chance of actually having the disease.

I'm picking 0.9% because, that's closest to my estimate and probably factors in the chance of it not even being in my 100 false-positives.

I believe I'm 9% likely to have it.

I want to say 99%, but it's probably not.

Well I think it's a trick question.

If I had the lethal disease, wouldn't I die within the week that it took the results to get to me? Looks like I don't have it after all and the test was wrong =)

Bill got the answer right. It's an example of anchoring, whereby you instinctively rely on one piece of information (in this case, the 99% accuracy) when making a decision and find it hard to stray from your own instincts (even if they're massively wrong).

Let's say that a million people take the test.

Statistically, there will be 100 people with the disease and 999,900 people without it.

Statistically, 1 out of the 100 people with the disease will be told they don't have it, whereas 9,999 of the people who don't have it will be told that they do.

That means that out of the original million, 10,098 people will be told that they have the disease, but only 99 of them will. The exact chance of you having the disease is 0.980392156862745% (which I rounded down to 0.9%).

Beats me.

I imagine the statistics of the accuracy of the test aren't relevant; it's actually the odds that I'm really the one person in 10,000 who has it. Although .9% doesn't seem small enough for that. So maybe it's a combination of that and likelihood that the test is wrong. At this point I am way over my head in terms of math and logic skills, though, so the answer is that I have no idea.

E none of the above because I am a healthy person and this is unlikely for me

99.9 % likely.

None of the above. I get tested a second time.

I'm 0.9% likely to have the disease

Fear, stress, negative thoughts can break down the body. The odds are against it, unless you have a hereditary propensity.

MAH BRAIN!!! IT HURTZ!!!

Not any more likely than anyone else in the general population.

None of the above.
Because....the chance that the disease was present in the first place is slimmer than before the test. Once the test was taken, the chances were higher. Seeing the poitive results made the chance 99% higher because the person due example is convinced, devastated...the emotional brain got involved and fudgeed it up for the rest of the body. Having a disease is different than seeing indications that there is something out of balance in the body and looking for healthier alternatives to health. Owning a disease is sad. Ignoring facts isn't good either. The mind will play tricks on the body if the two are not connected.

Before I was screened, I had a 0.01% chance of having the disease. Having received a positive result in a test where the sensitivity and specificity are both implied to be 99%, I would know that the positive predictive value of that result is 99% (so 99% of patients receiving that test result will actually have the disease). I've been trying to see where the trick is in this, but I'm clearly missing something unless it's somehow that individual risk remains the same after screening (i.e. 0.01%) as it was before, but that just seems silly. I can fiddle the numbers based on the information given so that the sensitivity is 100% and the specificity is 98%, but that still suggests I have a 98% chance of having the disease. The only other possble trick would be in the wording - that "accuracy" here is not quite what I am presuming...or that a "positive" result actually means "negative" for the disease.

Interested to read the answer...

This is why I shouldn't do maths at 2:30am after three days of exams... Using actual numbers to get my positive predictive value would have helped, rather than using percentages...I knew I was doing something silly because I'm well aware that the positive predictive value is low in rare diseases (which is why we don't bother screening for them).

E - None of the above


Cute, but unconvincing.

Fun survey!