Disease

Originally posted by BigDoggProblem
Hmm, not sure where 9% is coming from.

605 880 people will test positive. Of these, only 5 940 are actually infected. How is the answer not 0.98%?

It was 0.98% before the drinks, but it seems to spread quickly 😕

Originally posted by BigDoggProblem
Hmm, not sure where 9% is coming from.

605 880 people will test positive. Of these, only 5 940 are actually infected. How is the answer not 0.98%?

Um. The 9% comes from using the wrong numbers in the question (I originally worked this out using 60,000 infected people - that gives you an answer of ~9😵.

So: 60 million subtract 6000 = 59994000 people who are not infected.
The test will be correct for 99% of them, so it will say that 1%, ie 599940
are infected even when they aren't.
Of those that actually are infected the test will be right for 99% of the 6000 and will give 5940 of them as infected.
As BigDogg says, that gives 605880 who get a positive test result, but only 5940 are actually infected, so 5940/605880 = 0.009803922, which is 0.98%.

As I mentioned earlier, I like the counter-intuition here.

Originally posted by Diapason
Um. The 9% comes from using the wrong numbers in the question (I originally worked this out using 60,000 infected people - that gives you an answer of ~9😵.

So: 60 million subtract 6000 = 59994000 people who are not infected.
The test will be correct for 99% of them, so it will say that 1%, ie 599940
are infected even when they aren't.
Of those that ...[text shortened]... 80 = 0.009803922, which is 0.98%.

As I mentioned earlier, I like the counter-intuition here.

Would you take in to account the death rate from all other current diseases whilst accumulating these figures please. I'm getting confused.

Originally posted by Diapason
Um. The 9% comes from using the wrong numbers in the question (I originally worked this out using 60,000 infected people - that gives you an answer of ~9😵.

So: 60 million subtract 6000 = 59994000 people who are not infected.
The test will be correct for 99% of them, so it will say that 1%, ie 599940
are infected even when they aren't.
Of those that ...[text shortened]... 80 = 0.009803922, which is 0.98%.

As I mentioned earlier, I like the counter-intuition here.

Yeah, it is neat. 99% sounds like a good degree of accuracy for most things, but in this case the error rate of 1% is about 10,000 times bigger than the percentage of the population you're trying to test for. Stupid scientists...😠

So a test with 99% accuracy, results in your chances of being infected at 0.98% the way you all have explained it. I suggest this is incorrect.

What you meant to say is that there is only a 0.98% chance that you are NOT infected.


rounded up, this is 1% chance you are not infected and is no different than the intuitive answer that says 99% chance you are infected.

your nick says it all, I guess.

Originally posted by uzless
So a test with 99% accuracy, results in your chances of being infected at 0.98% the way you all have explained it. I suggest this is incorrect.

What you meant to say is that there is only a 0.98% chance that you are NOT infected.


rounded up, this is 1% chance you are not infected and is no different than the intuitive answer that says 99% chance you are infected.

No, it's written correctly. You have a very small chance of being infected even though the test gives the right answer 99% of the time.

You're interpreting this as "if the test says you are infected, you have a 99% chance of being infected." This is not what the problem states.

In the problem, 99% accuracy means "The result reported by the test is correct 99% of the time." Because so few people are infected, the test is *almost always wrong* when it reports that you are infected, but *almost always right* when if says you are not infected. Since the vast majority of people tested are not infected, the correct results outweigh the incorrect results and the test is correct 99% of the time, because most of the people tested aren't infected.

The reason for these counterintuitive results is that only one in a thousand people are infected in the first place. Imagine the following situation:

Say there's a one in a billion chance of your house being hit by a meteor while you're on vacation. You're worried about this, so you arrange for your neighbor to call you if your house gets hit by a meteor. Unfortunately, your neighbor gets drunk every night, and when he's drunk there's a 1% chance that he thinks your house has been hit by a meteor even if it hasn't been. And he can always tell when your house has been hit. So he's 99% accurate when he decides whether or not your house has been struck.

While on vacation, you get a call from your neighbor. He says your house has been hit by a meteor. What is the probability that your house has, in fact, been hit? Clearly it's still very small. It's much more likely that your neighbor is drunk and confused and your house is still standing. This is because there's such a small probability that your house will be hit by a meteor to begin with.

Now suppose there have been sudden hails of meteorites raining out of the sky, and there's a 25% chance that while you're on vacation your house will be hit by a meteor. The same situation applies with your neighbor: he's 99% accurate about meteor strikes. You get a call from him saying your house has been hit. What's the probability that he's right? This time it's 97%! The fact that there's a reasonable probability that your house really will be hit by a meteor means that the test is much more useful.

Originally posted by GregM
No, it's written correctly. You have a very small chance of being infected even though the test gives the right answer 99% of the time.

You're interpreting this as "if the test says you are infected, you have a 99% chance of being infected." This is not what the problem states.

In the problem, 99% accuracy means "The result reported by the test is corre really will be hit by a meteor means that the test is much more useful.

Ah, sorry my fault for reading the question wrong.

I thought the person was the last one tested and the stats had been determined based on results so far. I'm not in the UK so I took the sample set to therefore be 1 with a 99% accuracy.

My bad.