mike the wiz writes:
Imagine you had to get a heads on a coin toss one billion billion times consecutively.
Now, let's not go overboard on this thing, Mike. You don't need a billion billion consecutive coin tosses for what you're trying to demonstrate, just upending a bucketful of coins all at once is more than enough, and it's much easier to visualise.
The more important thing to note about your example is the mistake that you make by specifying in advance that all the coin tosses need to be heads. So, basically, you are saying that throwing a bucketload of coins on the floor and seeing them all end up heads is vastly improbable. But you forget that
any other outcome is equally improbable. Yet, when looking at the seemingly random mess of coins on the floor, nobody is going to be surprised. Because, after all,
some configuration
had to happen. It's only amazing if it happens
after you specify that exact configuration in advance, be it all heads, or any other permutation.
So, in conclusion: an event with a vanishingly small probability is not by definition impossible. A couple of hundreds of coins on the floor prove it.
"Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.