> I'm not certain how to calculate the odds, but I'm quite certain that the odds are astronomical. I wrote a brute force
> program to do the calculation, but it can't practically run past 2^24.
> 16 coin tosses have about 1 chance in 30 of getting a 75%/25% split. 24 coin tosses have about 1 chance in 100 of
> getting a 75%/25% split, and the odds get much, much worse as the number of tosses increases towards 2,000.
If you wanted to find out the probability that 2000 coin tosses would get 500 tails or less, you'd be better (I think) to find out the probability of getting at least 1500 heads (in no particular order).
I believe this is pretty easy. The chances of flipping 1500 heads where all other flips can be any combination of heads and tails should be something like:
0.5 ^ 1500 x 1.0 ^ 500 =
0.5 ^ 1500 =
2.85 x 10^(-452)
Basically, the probability (where certainty is one) of getting 1500 heads or more in a 2000 flip (or actually in any number of flips equal to or greater than 1500) dataset is a decimal point followed by four hundred and fifty-one zeros followed by 2851060965 (approximately). The chances of this happening are about one in thirty-five billion vigintillion vigintillion vigintillion vigintillion vigintillion vigintillion vigintillion, where a vigintillion is equal to one thousand decillion, where a decillion is equal to one thousand quintillion, where a quintillion is equal to one thousand billion.
In comparison, there are estimated to be "only" ten trillion vigintillion neutrons (or was it electrons?) in the universe. The ratio of the inverse of the above probability and the number of neutrons in the universe is probably greater than the ratio of the size of the local galactic cluster to the size of your spleen.
Apologies if I misdid the math. I think I have it more or less correct. :)
And this exercise is only meant to show that Scumbria's hypothesis about flipping 500 tails or less in a 2000 flip contest being astronomically small was a conservative statement. However, this post is not meant to confirm or deny Scumbria's suggestion that this has any relation to the current political episode. Assuming I didn't do something insanely major in my above math, I may followup on that further point, but I dunno if I want to make me into flamebait. <g>
-JC |
