SSDD – Same Stuff, Different Darwinist. This time someone said at skeptical zone:
if you have 500 flips of a fair coin that all come up heads, given your qualification (“fair coin”), that is outcome is perfectly consistent with fair
So if someone has 500 fair coins, and he finds them all heads, that is consistent with expected physical outcomes of random flips? 😯 I don’t think so!
Correct me if I’m wrong but if you have 500 fair coins, the expectation is 250 coins will be heads, not 500. Now if you have 261 of the 500 coins heads, that is still within a standard deviation of expectation, and thus would still be a reasonable outcome of a random process. But 500 coins heads out of 500 fair coins? No way!
p = probability of heads: 0.5
n = number of coins: 500
Then the standard deviation for binomial distributions yields:
So 261 coins heads is (261 -250)/11 = 1 standard deviations (1 sigma) from expectation from a purely random process of coin flips.
So 272 coins heads is (272 -250)/11 = 2 standard deviations (2 sigma) from expectation from a purely random process of coin flips.
So 500 coins heads is (500-250)/11 = 22 standard deviations (22 sigma) from expectation! These numbers are so extreme, it’s probably inappropriate to even use the normal distribution’s approximation of the binomial distribution, and hence “22 sigma” just becomes a figure of speech in this extreme case…
There are many configurations that are 250 coins heads. The number is:
, thus there are many coin configurations most consistent with the expectation of 250 coins heads (50%), whereas only 1 configuration of all heads for the least consistent behavior for a fair coin.
Bottom line, the critic at skeptical zone is incorrect. His statement symbolizes the determination to disagree with my reasonable claim that 500 fair coins heads is inconsistent with a random physical outcome.