Alanna Thousands Valley wrote: » The coin (over 'large' datasets) does indeed average out very close to 50:50. Many (slow, boring) trials have already been done to support it such as:
Fourier wrote: » Trust me it's not as clear cut as you think. It's very hard to defend probability as anything other than a betting weight in our heads rather than something out there in the world. As I said, if you learn more about the coin, then conditioned on that you'd change it to 90:10, it's no longer 50:50.
Fourier wrote: » Alanna Thousands Valley wrote: » The coin (over 'large' datasets) does indeed average out very close to 50:50. Many (slow, boring) trials have already been done to support it such as: Trust me it's not as clear cut as you think. It's very hard to defend probability as anything other than a betting weight in our heads rather than something out there in the world. As I said, if you learn more about the coin, then conditioned on that you'd change it to 90:10, it's no longer 50:50. If you want I can discuss this on the maths forum, but if you want to read up on it I'd have a read of the works of Edwin Thompson Jaynes and Bruno de Finetti. Their works are the main reason mathematicians don't view probability the way you're talking about (known formally as Frequentism)
Realt Dearg Sec wrote: » Is this just a problem with the coin? I presume we are using the coin as a kind of easily visualisable image of a one or the other situation. If it was a random number generator that could send up a 1 or a 0 each time would that be closer to what we're describing as heads or tails?
Alanna Thousands Valley wrote: » Fourier would seem to deny the law of large^ numbers if suggesting 90:10.
Fourier wrote: » I'll start a thread on the Maths forum based off Realt Dearg Sec's post.
Alanna Thousands Valley wrote: » The folks in Vegas sure don't like card counters at the BlackJack table.
quickbeam wrote: » Another one is Benford's Law. You'd think that of all the numbers in the world, they'd all have an equal likelihood of appearing in everyday life. Eg, the 10,000 numbers between 1 and 10,000 should all have a 1 in 10,000 chance of appearing, ie the number 1,899 would have the same chance as the number 8,199 (say). But no, Benford's Law states that numbers beginning with lower digits have a far higher chance of appearing than those of lower digits. 1,899 more often than 8,199. But 18,990 also more often than 8,199.
quokula wrote: » Benford's Law doesn't state that numbers with lower first digits are more likely, but simply that lower first digits are more likely, which is a small but important difference. This is because there is almost always more numbers starting with a lower digit in a given data set. E.g. if there is a 1 in 1500 chance, then [1,10-19,100-199,1000-1500] all start with 1, but only [8,80-89,800-899] start with 8 - so you've a much higher chance of a number starting with 1 than a number starting with 8, but you don't have a higher chance of any particular number like 189 compared to 891. In your specific example of 1-10,000 then the chances of it beginning with 1 or 8 are nearly identical (they would be identical for 1-9,999), but the law is based on observations in the real world where the range is not defined and is very unlikely to be a precise round number like that.
Alanna Thousands Valley wrote: » Young, cheery, pop singer 'Anne-Marie' (xmas number 1's and recent duo with Ed Sherry) - is also a 'triple-time Karate 空手道 World Champion'.
GBX wrote: » The town of Büsingen am Hochrhein is a German town completely surrounded by Switzerland. It doesn't use the Euro - it unofficially uses the Swiss Franc.
quokula wrote: » Benford's Law doesn't state that numbers with lower first digits are more likely, but simply that lower first digits are more likely, which is a small but important difference. This is because there is almost always more numbers starting with a lower digit in a given data set.
Candie wrote: » There are unsubstantiated claims that during the Cultural Revolution the shortage of cow bone led to the ash of cremated human bones being included in the production of bone china.
Capt'n Midnight wrote: » During the early days of Railways in Egypt they burned Mummies for fuel
DEFTLEFTHAND wrote: » Yes. The company was founded in the 1800s and has been involved in a vast array of different ventures in its history. Paper mills, rubber products, hospital equipment.
Chancer3001 wrote: » Whenever I read stuff like that bone China thing I remember how a really useless I'd be if I travelled back in time. All id have is good geography and know that America was there! Maybe emphasise how important sanitation is. But I couldn't help in any practical ways.