a statistics question

[Monkeyleg]

Let's say that 325 out of every 100,000 have ingrown toenails every year. How many people would you have to meet in 6 months time to meet two people with ingrown toenails?

Despite being very good at the math sciences, I was never any good at this.

[MrsSmith]

That's pretty simple math. But ... why???

[birdman]

You actually need another piece of information...how long the average ingrown toenail lasts. 

[makattak]

As birdman says. I can tell you you'd meet two people who have had an ingrown toenail in the past year if you meet just a little under 700 people. (I don't feel like working out the exact number in my head.)

(I should also have put the word "on average" in there. Of course any sample can be high or low.)

[Monkeyleg]

What I'm trying to figure out is what the odds of of encountering two people with ingrown toenails in one year. I know that would require a sample size of the number of people you meet, but I'm trying to work backwards. I'm trying to figure out, based on the 325/100,000 number, what the odds are of meeting two people with ingrown toenails based upon a sample size of X.

Or am I not thinking about this the right way? It seems like odds of 1 in 700 would be too low.

[makattak]

What I'm trying to figure out is what the odds of of encountering two people with ingrown toenails in one year. I know that would require a sample size of the number of people you meet, but I'm trying to work backwards. I'm trying to figure out, based on the 325/100,000 number, what the odds are of meeting two people with ingrown toenails based upon a sample size of X.

Or am I not thinking about this the right way? It seems like odds of 1 in 700 would be too low.

2 in 700. One in ~350ish. Just for people that have had one in the past year.

As I am somewhat prone to them, having inherited that from my mother, I would be willing to bet that those prone to ingrown toenails are not randomly dispersed through the population though.

[Waitone]

Waaay too much time on his hands.

[cordex]

There's more to the story.  Most importantly, ingrown toenails are not randomly spread across the population.  People with genetic predispositions to getting them, poor foot hygiene, who cut their nails in certain ways, whose feet tend to stay damp, who have toenail fungus, who wear tight shoes, etc. will tend to be more inclined to get ingrown toenails.  

A real calculation of statistical likelihood would have to take into account that people tend to associate with those who share similar lifestyles and thus if their lifestyle encourages risk factors they might be more likely to tend to get ingrown toenails than the average population.

Is this some new moccasin marketing idea?  "If you trade in your cowboy boots for Monkeyleg Moccasins you are 67.4% less likely to get ingrown toenails."

edit: Mak beat me to it ...

[Monkeyleg]

It's not about ingrown toenails, but I can't say what it is. I was just using that as an example.

So, if a person meets 200,000 people, there's a theoretical odds of 1:700 that he would meet two people with the toenails or whatever I'm looking at (teal blue eyes, etc).

Does it then follow that meeting 100,000 people means odds are 1:1400, meeting 50,000 means odds of 1:2800, 25,000 means odds of 1:5600, etc? I always thought that figuring odds was more complicated than that.

[makattak]

It's not about ingrown toenails, but I can't say what it is. I was just using that as an example.

So, if a person meets 200,000 people, there's a theoretical odds of 1:700 that he would meet two people with the toenails or whatever I'm looking at (teal blue eyes, etc).

Does it then follow that meeting 100,000 people means odds are 1:1400, meeting 50,000 means odds of 1:2800, 25,000 means odds of 1:5600, etc? I always thought that figuring odds was more complicated than that.

I the theoretical odds are such for 200,000, then, yes it is that simple. You are changing the denominator without changing the numerator.

[Fly320s]

It's not about ingrown toenails, but I can't say what it is. I was just using that as an example.

So, if a person meets 200,000 people, there's a theoretical odds of 1:700 that he would meet two people with the toenails or whatever I'm looking at (teal blue eyes, etc).

Does it then follow that meeting 100,000 people means odds are 1:1400, meeting 50,000 means odds of 1:2800, 25,000 means odds of 1:5600, etc? I always thought that figuring odds was more complicated than that.

I wouldn't think so. Don't the odds stay the same no matter the sample size?

[makattak]

I wouldn't think so. Don't the odds stay the same no matter the sample size?

Odds of meeting said person within the sample do not change.

Odds of meeting that person if you meet X number of people where X= X₁, X₁/2, X₁/4, X₁/8, etc... will change.

[makattak]

Also, your original question and your second question are at odds, Monkeyleg.

In the first one, you gave the number of people per 100,000 with an affliction.

In the second one your numbers are odds of meeting a person with that affliction.

These are two different (but related) concepts, and I answered them separately. Were you thinking they were the same concept?

As in: if you meet 700 people, on average you should meet 2 with the original affliction.

If you meet 200,000 people and have a 1 in 700 chance of meeting that person after meeting 200,000 people, that is an EXTREMELY rare affliction.

Did you mean to change the question with your second post?

[RoadKingLarry]

Lies, damned lies and statistics.

[Monkeyleg]

Yeah, RoadKingLarry, I didn't phrase my question properly.

I was thinking about something personal (hence the references to toenails and other related stuff), and just got to wondering what the odds are of meeting two people with the same somewhat rare condition, much less one. Most people don't have thousands or even hundreds of friends, so it would seem to me that the odds of having two friends with the same condition would be very high.

If you break down the 325 out of 100,000 into a smaller subset of people (say Irish people have more instances of ingrown toenails, and you know a ton of Irish people, just for the hell of it), then the odds become less steep.

[vaskidmark]

and you know a ton of Irish people, just for the hell of it

And why else would anyone who is not living in Ireland know a ton of Irish people? 

stay safe.

[Monkeyleg]

And why else would anyone who is not living in Ireland know a ton of Irish people? 

NYC cops, people who drink a lot or fight a lot (or both)...