Annoying Questions I'd Like Answered...

Post by **fbmf** » Sun Aug 31, 2014 2:46 am

I roll a die with 365 sides (go with it) 74 times. I get results of 1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,8,10,10,11,11,12,12 then fifty more results that are not those numbers. What are the odds of this?

Game On,
fbmf

Sam · Post by **Sam** » Sun Aug 31, 2014 2:52 am

The odds of that exact sequence is (1/365)^24 * (353/365)^50

Shiritai · Post by **Shiritai** » Sun Aug 31, 2014 2:58 am

Should be (1/365)^24*(353/365)^50, since it's a 1/365 chance for each of those 24 exact numbers and a 353/365 chance of getting a 13-365 result on the last 50 rolls.

Edit: aaaaand ninja'd.

TiaC · Post by **TiaC** » Sun Aug 31, 2014 8:16 am

They are of course assuming that your rolls are ordered.

Post by **fbmf** » Sun Aug 31, 2014 1:11 pm

And if they aren't in any particular order?

Game On,
fbmf

Username17 · Post by **Username17** » Sun Aug 31, 2014 1:57 pm

fbmf wrote:And if they aren't in any particular order?

Game On,
fbmf

Then you multiply that extremely small chance by the extremely large number of possible orders they could be arranged in.

In this case, that number would be 74!/2!/2!/2!/2!/2!/2!/2!/2!/2!/2!/2!/2!/50!

-Username17

Laertes · Post by **Laertes** » Sun Aug 31, 2014 2:02 pm

fbmf wrote:And if they aren't in any particular order?

Game On,
fbmf

If you don't care about the order, then multiply that probability by
74! / 50!

That is, multiply it by 74 * 73 * 72 * 71 * 70 * ... * 52 * 51 * 50. Which is approximately 10^53.

Edit: ninja'd. Frank, you don't need to worry about the 2^12 because the P(n,r) function handles that for you.

momothefiddler · Post by **momothefiddler** » Sun Aug 31, 2014 3:38 pm

rolling 2,3,3 on a d6 is 1/6^3 ordered, and 3!/(6^3*2!) unordered because there are only 3 possible orderings of that, not 6.

My point is that you do need the 2^12. Oh no, a whole four orders of magnitude.

Also, I take it we're assuming this was a typo?

8,8,9,8,

Because if not, it's (363^50*74!)/(365^74*50!*2^10*3) instead of (363^50*74!)/(365^74*50!*2^12)

fbmf: when you say "fifty more results that are not those numbers", do you mean that none of those fifty rolls come up 1-12, or just that there are 50 more numbers you don't care about? Because these probabilities have all been assuming the former, and if it's okay to have at least two 4s rather than exactly two 4s, that increases the chances dramatically makes a minor change but leaves it essentially impossible wow my estimate was way off.

In any case, the answer is in the neighborhood of 10^-24.

Post by **fbmf** » Sun Aug 31, 2014 4:07 pm

Momo,

That was a typo, and I mean the other fifty results are not 1-12.

Game On,
fbmf

momothefiddler · Post by **momothefiddler** » Sun Aug 31, 2014 4:13 pm

Okay. Then you get (363^50*74!)/(365^74*50!*2^12), which is around 6*10^-23, or about 1 in 15,496,195,176,257,272,899,969.

fectin · Post by **fectin** » Sun Aug 31, 2014 10:49 pm

I think the interesting question is what are the odds, by sequence length, of a sequence of numbers where each number is equal to or one more than the previous number. Bonus credit if your solution is for an originally-unordered sequence.

momothefiddler · Post by **momothefiddler** » Sun Aug 31, 2014 10:56 pm

fectin wrote:I think the interesting question is what are the odds, by sequence length, of a sequence of numbers where each number is equal to or one more than the previous number. Bonus credit if your solution is for an originally-unordered sequence.

Eh? Maybe I'm missing something, but at that point aren't you just asking the odds of a sequence that can be rearranged in ascending order?

Also, do you have a die size in mind? Or an arbitrary-but-finite die size? If you just mean randomly selecting from all positive numbers, the answer is sort of 100%, but is actually "you can't do that".

fectin · Post by **fectin** » Mon Sep 01, 2014 2:01 am

Yes, but that's what fbmf was asking about (365 sides, rolled 74 times). Odds of a sequence in order are fairly easy, odds of an orderable sequence are rough.

momothefiddler · Post by **momothefiddler** » Mon Sep 01, 2014 2:18 am

Oops. I read "or one more than" as "or more than", in which case it's a trivial ordering. Sorry.

...Yeah, no, I don't have any solution for that.

erik · Post by **erik** » Mon Sep 01, 2014 2:40 am

I theorize that fbmf has discovered among a group of 74 people, that 24 of the birthdays are in pairs of 12 consecutive days that recently came to pass.

Incidentally, birthdays are not evenly distributed, here's a representation of US birthday stats

More people make babies at certain times and doctors avoid delivering on holidays (weekends too, but those roll around).

TiaC · Post by **TiaC** » Mon Sep 01, 2014 3:04 am

I wonder if it's superstition that causes the drop on the 13th?

I knew that there was a big jump in September, it causes there to be fewer holidays then historically.

Kaelik · Post by **Kaelik** » Mon Sep 01, 2014 4:06 am

Those spikes one week apart in April are representative of my person experience. Everyone I know with a birthday in April is on the 1st, 8th, 15th, and 24th. So not literally 1 week between, but that is how it is, and it's just weird.

Username17 · Post by **Username17** » Mon Sep 01, 2014 5:32 am

Kaelik wrote:Those spikes one week apart in April are representative of my person experience. Everyone I know with a birthday in April is on the 1st, 8th, 15th, and 24th. So not literally 1 week between, but that is how it is, and it's just weird.

My sister and I are born on the same day in April and it is none of those days.

-Username17

Post by **fbmf** » Mon Sep 01, 2014 12:22 pm

erik wrote:I theorize that fbmf has discovered among a group of 74 people, that 24 of the birthdays are in pairs of 12 consecutive days that recently came to pass.

A fellow educator in my game night group noticed it on her roster for the school year that just started. She asked aloud, "What are the odds?"

Game On,
fbmf

erik · Post by **erik** » Mon Sep 01, 2014 1:38 pm

And when it is the same age then weekends do matter and it makes it even more likely to share birthdays.

So... a lot less unlikely than the stats quoted previously would indicate.

To know how much less would probably require the time of an actuary with lots of tables I don't have access to.

Laertes · Post by **Laertes** » Mon Sep 01, 2014 1:49 pm

I mentioned this problem to the members of my gaming night last night and we were wondering about what the instigation of it was, actually. It's good to know.

Kaelik wrote: Those spikes one week apart in April are representative of my person experience. Everyone I know with a birthday in April is on the 1st, 8th, 15th, and 24th. So not literally 1 week between, but that is how it is, and it's just weird.

I have heard, anecdotally, that clustered births can be tracked very accurately to unusually cold nights or power cuts nine months beforehand. If we were to dig up the meteorological and power data 283 days before those dates (that is, on 25 June or 2, 9 or 18 July) there might be a correlation.

Kaelik · Post by **Kaelik** » Mon Sep 01, 2014 2:52 pm

FrankTrollman wrote:
Kaelik wrote:Those spikes one week apart in April are representative of my person experience. Everyone I know with a birthday in April is on the 1st, 8th, 15th, and 24th. So not literally 1 week between, but that is how it is, and it's just weird.
My sister and I are born on the same day in April and it is none of those days.

-Username17

My whole world is a lie! Also, you and your sister were born on the same day? Do you have a twin? Or did your parents have a very regular sex life?

Laertes wrote:I have heard, anecdotally, that clustered births can be tracked very accurately to unusually cold nights or power cuts nine months beforehand. If we were to dig up the meteorological and power data 283 days before those dates (that is, on 25 June or 2, 9 or 18 July) there might be a correlation.

The people I know who were born in April are several years apart. So... nope.

Maj · Post by **Maj** » Wed Sep 03, 2014 6:34 pm

Is there any validity to this comparison of the types of food eaters in the world?

http://www.vegsource.com/articles2/anatomy_mills.htm

OgreBattle · Post by **OgreBattle** » Wed Sep 03, 2014 6:44 pm

So Battlestar galacticaha has a mono-eye visor for their cyclons

Were they the first to do that? The series came out in 1978 but did Cyclons apear first thing?

I'm trying to figure out if Gundam (1979) was inspired by that for the Zaku design, or if there was something older.

Username17 · Post by **Username17** » Wed Sep 03, 2014 7:14 pm

The Day the Earth Stood Still, 1951

Edit:

Maj wrote:Is there any validity to this comparison of the types of food eaters in the world?

http://www.vegsource.com/articles2/anatomy_mills.htm

No. That is bizarre vegetarian propaganda. Whether animals have well developed jaw muscles or not has fuck-all to do with whether they are herbivores or carnivores, and everything to do with how tough the things they expect to be eating are. Creatures that eat shelled animals have monstrous jaw muscles, and creatures that eat soft fruit have weak jaw muscles. Creatures that eat soft flesh and leave bones have weak jaw muscles, and creatures that eat wood have powerful jaw muscles. Vitamin A is not binarily "detoxified" or not, there's a range below which you don't have enough and above which you have too much. Your body is able to metabolize and excrete vitamin A, so I have no idea what "cannot detoxify vitamin A" is supposed to mean in any context. All animals suffer hypervitaminosis A from some levels of vitamin A, whether they are carnivorous or not.

Every part of that chart is insane, and none of the claims made on any part of it are true. I wouldn't be at all surprised if the person credited with making it is either not a real doctor or doesn't even exist.

-Username17