If you're bored see if you can answer this one...

IdleHans

There is a symptomless disease carried by 1% of the population. A test has been developed to detect the disease, and the test is 99% accurate, whether positive or negative.
If an individual shows a postive result, what is the probability that the individual has the disease?

guinnessaddick

99%

IdleHans

nope. The answer is surprising (or I wouldnt have bothered).

Addicted

Or if you're asking whats the chance they've got the disease and the test is accurate when testing it's 0.99%

Addicted

Just realised I always jump in and I'm always wrong. FML

bobmunro

Probability 0.99 - 99%

randy andy

I want to say 98.02%, but I haven't got time to do the maths to corroborate that figure

bobmunro

0.01

paulbaconsarnie

Probability is 0.01
The test isn't absolute so the probability doesn't change.
I usually get these things wrong though.

Low_Ears

50% - just as likely to have aninaccurate result as have the disease

IdleHans

Well done, Low Ears. Spot on.

thai malaysia addick

50%

bobmunro

Not sure about this 50% malarky - agree with @paulbaconsarnie

If the statement of 1% have the desease is correct then the test probability is irrelevant - they are not related probabilities.

Bayes theorum is at work and it's similar in principle to the Monty Hall paradigm.

IdleHans

Surely they are related probabilities. The question is what is the chance of someone who has a positive result actually having the disease, not what is the chance of someone having the disease. Clearly the latter is 1%, as that is given in the first sentence of the question.

foxjam

Surely the test accuracy is the only relevant information here. The answer must be 99%. The test accuracy means that the test gives (on average) 99 correct results out of 100. Given 100 positive results, one would expect 99 of them to be correct which implies a 99% probability of having the disease when given a positive result. It's possible that I've missed something, but have you got a source for this?

foxjam

Having said that I realised I did miss something. It's 99 out of 100 results are correct, not necessarily 99 out of 100 positive results. So given 100 people take the test, one would expect 1 false result and 1 person to actually have the disease. I can see where the 50% comes from given that a positive result would suggest either the false result or having the disease in equal probability.

IdleHans

Foxjam, you're right so far as you've gone.

Let's assume the population is 10,000. Of these 100 (1%) will have the disease. The test is 99% accurate, so the results will be 99 positive and 1 negative.
9,900 (99%) will NOT have the disease. The test for them will show 9,801 correct negative results and 99 false positive results.
Thus in total 198 will test positive, but only 99 will actually have the disease. Thus even with a 99% accurate test, if an individual has a positive result the chance of them actually having the disease is only 50%.

colthe3rd

Yeah not sure you worded the question correctly there.

kings hill addick

foxjam said:

Having said that I realised I did miss something. It's 99 out of 100 results are correct, not necessarily 99 out of 100 positive results. So given 100 people take the test, one would expect 1 false result and 1 person to actually have the disease. I can see where the 50% comes from given that a positive result would suggest either the false result or having the disease in equal probability.

Have you factored in the possibility of the 1% inaccurate result applying to the positive result? Thus you could have 99 negatives and one positive, in which case the probability would, presumably, be 0% that the positive result was, in reality, positive, if there has to be one, and only one, inaccurate result. The 50% only applies to two positives in a sample of 100. However as the question doesn't give a sample size I don't see how one can extrapolate to 50% in either scenario.

foxjam

I did think about that, if the false result is also the person with the disease then all of the 100 people get negative results. Given that the person in question gets a positive result, (I think) we can discard this scenario and say there is one other positive result. This question seems to be one step away from being incredibly involved.

bobmunro

https://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml

foxjam

bobmunro said:

https://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml

So the question we have here is essentially a special case of the one you just posted, but here the probability of a false positive is the same as the probability of having the disease.

Fiiish

Essentially it is 50% if you think about it.

99% of the population won't have the disease, but 1% of that 99% will display a false positive, so 0.99% of the whole population will have a positive result but not actually have the disease.

Also, out of the 1% that have the disease, 99% will show as a positive, so 0.99% of the population will have a positive result and have the disease.

So it is 50/50, as 98.01% of the population will correctly show a negative result and 0.01% of the population will incorrectly show a negative result. That all adds up to 100%.

I think I have that right!

ForeverAddickted

This thread has made my head hurt

AddicksAddict

The working out given by @IdleHans, above, uses a population of 10,000 to derive the answer. So, consider this:

If you're marooned alone on a desert island, so the population sample is one, does that affect the result? (I know the answer, I'm just wondering what others think.)

Bryan_Kynsie

I would want a second opinion. Whats the position if the individual takes the test again and it comes out positive again?

rikofold

If it says it's positive, the chances of you having the disease is 99% because the test is 99% accurate: if it says it's positive, it's right 99 times out of 100.

The question is badly worded. I suspect it intends to ask, what's the chance of having the disease and the test showing it up? Quite different. In that case it's 1% (chance of having the disease) x 99% chance of the test showing it up, which is 0.99%.

bc_addick

I believe that 100% of Lifers who read this thread will get a headache.

tangoflash

An easier one for you all...................

Fiiish

87

3blokes

I'm worried I've caught this.
Infected of Maidstone