I preface this by saying math is not my strong suit.
Suppose 1 person in 100,000 gets disease X in general.
Suppose further that 1 person in 100,000 who get disease Y will develop disease X.
Does that mean if you get disease Y, you have a 2 in 100,000 chance of getting disease X? Why or why not?
And how rare is a disease that only 1 in 100,000 get considered, medically and statistically? (Numbers and imagining measurements are not my strong suit.)
Divide humanity into two parts: those with Y and those without Y. Those with Y have a 1 in 100,000 chance of getting X. Those without Y also have a 1 in 100,000 chance of getting X. Therefore, no matter who you are, your chances of getting X are 1 in 100,000.
You can think of this in terms of conditional probability. With the “|” symbol meaning “given that”, we can write
P(X) = 1/100,000;
P(X|Y) = 1/100,000; which is actually what you’re asking when you say
Saying, “if you get disease Y” is the same thing, probabilistically, as saying “given disease Y”. So if you get disease Y, you have 1/100,000 of developing X, by your original assumptions.
From the information in the OP, we can conclude that whether you have disease Y has no effect on whether you’ll get disease X. This is what we refer to as probabilistic independence, which is a pretty strong condition. If anyone’s tracking how many people with a given disease get another disease, you can be pretty sure you won’t see numbers like this.
Are you sure you are framing the question correctly? As ultrafilter points out, in the question’s current form, the presence or absence of disease Y is immaterial (which is an unlikely case).
I hope it’s not too early in the thread to tell my second favorite joke, which I believe I first read years ago here on the dope.
A group of epidemiologists and a group of biostatisticians are both going from Boston to Philly for a public health conference. Both groups decide to take the train. When they get to the train station in Boston, each of the epidemiologists has a ticket, but they notice that the biostatisticians have but one ticket among them. “How do you ever think you’ll all get to Philly with just one ticket?” the epidemiologists ask. “We have our methods,” reply the statisticians.
They get on the train and after a while they hear the conductor coming down the aisle asking for tickets. Suddenly, all the statisticians jump up out of their seats and run into the tiny lavatory at the back of the car. When the conductor enters the car, he notices the “occupied” sign on the lavatory, knocks on the door, and says, “Ticket, please!” The door cracks open, the statisticians slide out the ticket, the conductor punches it and slides it back. After he goes into the next car, the statisticians come out of the lavatory and go back to their seats, grinning smuggly at the epidemiologists.
After the conference, both groups meet back at the train station in Philadelphia. Of course, the epidemiologists have only bought one ticket this time, but they see that the biostatisticians have NO ticket whatsoever. “How do you ever think you’ll get back to Boston without any ticket?” ask the epidemiologists. “We have our methods,” reply the statisticians.
Once on board the train they again hear the conductor coming, and all of the epidemiologist jump up out of their seats and crowd into the tiny lavatory in the back of the car. The biostatisticians jump up and crowd into the other tiny lavatory across the aisle, all except one, who knocks on the door of the lavatory containing the epidemiologists, and says “Ticket, please!” The epidemiologists crack open the door and slide out the ticket, which the statistician grabs, then she runs into the other lavatory with all the other statisticians and closes the door just as the conductor enters the car.
Obviously, the biostatisticians return to Boston safely, while the epidemiologists are all thrown off the train in Newark. The moral of the story is: Never attempt to apply statistical methods until you understand the underlying principles.
I’m pretty sure that the question is misstated. Although if he meant those that have Y have an additional 1 in 100,000 chance, then the question is trivial as well.
I think the question he’s looking for is something along the lines of: If a person has disease Y or Z they have a 1 in 100,000 chance of getting disease X. What’s the chances a person that has both Y and Z gets X. Which is much harder to say. We don’t know if the two are independent or whatnot.
:D:cool:
Yyyyeah, let’s go with that. 
(The original post was indeed a misstatement/misunderstanding. Let’s go with this interpretation of the question. :))
ETA: And if you like, answer my last question, which is NOT misstated, but is sort of an aside - although it certainly fits the thread title.
Alan, I chuckled a bit when I read that joke. And then I opened the spoiler, and absolutely guffawed. Well-played.
Thanks! That gives me a warm feeling inside.
I wish I could remember where I got it from. It was either a very early thread here on the SDMB (probably unsearchable) or possibly it was from my friend Max Blair (who I haven’t spoken to since college, but it wouldn’t suprise me if he reads the Dope). Or it was from someone else.
Well, if they’re not independent, then we don’t know without more information.
If they are, then it’s 1-(99,999/100,000)^2 which is slightly less than 2 in 100,000.