Actual photons

what statistics says is if you flip a fair coin 2 million times then the
fraction of heads will be very close to 0.5 but the difference between the
number of heads and the number of tails is not zero and can grow to a very
large number when the number of flips is 10 or 20 million or more. I think this
is related to the gambler's ruin problem.
hope this helps
anton


In article ,
says...

Here is my result: 8 heads, twelve tails.

You have a biased coin

HAVRILIAK says...

Here is my result: 8 heads, twelve tails.

You have a biased coin

Put up or shut up. Take your own coin and flip it 20 times.
repeat the experiment with 4 different coins. Use a penny,
nickel dime, and quarter to insure that the US Mint isn't
slipping you biased coins Report the results.

If you continue to refuse to do the experiment, everyone will
laugh at you for being willfully ignorant and ineducable.

Martin Brown says...

Your [HAVRILIAK's] calculation is based on a wrong assumption.
I suggest you *really* go and try this yourself with a genuine coin

I predict that he will spend several hours arguing rather than spend
ten minutes flipping coins.

(HAVRILIAK) writes:

Here is my result: 8 heads, twelve tails.

You have a biased coin

You cannot make that conclusion since, even with a fair coin, there is
a reasonably high probability of obtaining that result or worse. With
20 tosses the probabilities of obtaining 0 to 20 heads (or tails) can
be calculated from the binomial distribution and is as follows:

Heads Probability
0 0.00000095
1 0.00001907
2 0.00018120
3 0.00108719
4 0.00462055
5 0.01478577
6 0.03696442
7 0.07392883
8 0.12013435
9 0.16017914
10 0.17619705
11 0.16017914
12 0.12013435
13 0.07392883
14 0.03696442
15 0.01478577
16 0.00462055
17 0.00108719
18 0.00018120
19 0.00001907
20 0.00000095

So, the probability of getting exactly 10 heads is just 0.176 and to
get something else is 1-0.176 = 0.824, even with a perfectly fair
coin.

pej
--
Per Erik Jorde

"Richard F.L.R. Snashall" wrote:

Here is my result: 8 heads, twelve tails.



You have a biased coin


Prove it!

It was made by a government.

QED

--
Martin Frey
http://www.hadastro.org.uk
N 51 02 E 0 47