Testing random

[Chris Angelico]

On Mon, Jun 8, 2015 at 4:28 AM, Steven D'Aprano <steve at pearwood.info> wrote:
> If my previous post didn't convince you, consider an even simpler random
> distribution: tossing a fair coin. The probability of getting a head is
> exactly 1/2 whether you toss the coin once or a thousand times. But if you
> toss the coin once, your chances of getting "no heads" is 1/2. If you toss
> it a thousand times, your chances of getting "no heads" is 1/2**1000.

Although... purity and reality do sometimes disagree. The concept of
"independent events" says that if I toss a coin 99 times and it comes
up heads every time, the probability that it'll come up heads again
the hundredth time is still 50-50. But the reality of cheats coins
says that the chances of the coin being a fair one and having been
tossed 99 times and come up heads every time is one in 1<<99, and
given that the mass of this planet is roughly 6E27 grams, that would
mean that you'd need about a thousand earths' worth of coins to get
that many... so the chances are much better that you're looking at
either an imbalanced coin or a crafty operator, and the probability is
much higher that it comes up heads :)

ChrisA