### What's the probability you live in an odd numbered house?

A video of me reading my original blog post out loud http://singingbanana.tumblr.com/post/6629627960/whats-the-probability-you-live-in-an-odd-numbered The original Facebook poll: https://www.facebook.com/home.php?sk=question&id=218841344812765&qa_ref=qd ---------------------- More details: The answer 0.502 falls outside what you would expect with 400000 coin tosses, with 95% of such experiments being within 200000 +/- 300. Therefore the difference 0.002, although small, is statistically significant. That is to say, extremely unlikely to be a simple variation due to chance, but a genuine difference. The conclusion is strong since 400000 is a large sample. Using our data we have seen the answer appears to 0.502. And we have shown that answer is statistically significant. But justifying why it's 0.502 is more difficult. I suggest in the video that there are more odd numbered houses due to streets with an odd number of houses. An argument that works brilliantly if the houses are in a row, or on a close, or a block of flats. If the street has odd numbered houses on one side and even numbered houses on the other side, I am assuming that the majority of streets with. say, 100 houses have 50 houses on the even side and 50 houses on the odd side. But if the street had 101 houses I am assuming the majority have 51 on the odd side and 50 on the even side. This allows the numbering to be consecutive, and would be strange otherwise. For the same reason, if one side has a few more houses than the other side, I can imagine the long side will be the odd numbered side. If that it is not true, it doesn't change the fact that the statistical analysis shows the answer *is* 0.502, and we have already come up with enough reasons to explain it. [Edit: That was my guess about two sided streets - and it may not be true! Here's a wikipedia article about house numbering http://en.wikipedia.org/wiki/House_numbering Houses are numbered with odd houses being on the left/right (depending which country it is) as you look up the street with houses in ascending order. As I said before, the statistics show that there are more odd numbered houses than even numbered houses, justifying that is secondary.] A rough calculation might be to work out the average proportion of odd numbered houses in streets of size 1 to 1000?. That is 1/1000 sum (4k -1)/(4k-2) summing from 1 to 500. Which is 0.502. This is rough because it assumes the distribution of street sizes is uniform. We do not know what the true distribution is, only that it gives us an average of 0.502. I believe exceptions will either be insignificant (e.g. houses without the number 13), or cancel each other out (e.g. streets with only odd numbers cancelling out with streets that only have even numbers). [Edit: Here's a BBC piece about houses numbered 13 http://news.bbc.co.uk/1/hi/magazine/7779212.stm] Whatever the truth, the statistical analysis shows that the average appears to be 0.502, with justifying that answer being secondary.

Length:
06:38