Life is not improbable.

[Chas]

If you have an infinite number of trials, by definition you'll exhaust every possibility.

Negative Esquilax.

Some infinities can be insufficient.

Imagine a circle. Now imagine an infinite number of rays originating at the center of the circle and passing thru every point that makes up the perimeter. At the perimeter those rays, as they pass thru each point which makes up the circle are "touching each other". However once they go beyond the perimeter those rays continue to diverge. The farther away from the perimeter the more diverged from each other those rays become. So far so good?

Now draw a larger circle around the first one. There are an infinite number of rays coming from the smaller circle but that infinite number of rays is insufficient to go thru every point that makes up the perimeter of the larger circle. In that space between the divergent rays will exist points that make up the larger circle that have no rays going thru them.

You would think that because you have an infinite number of rays...you would have enough to go thru all the points that make up the larger circle....but you do not.

You don't seem to know the difference between countable and uncountable infinities.

It is assumed that when talking about white balls/red balls, we are talking about countable infinities, the infinity of the natural numbers.

The infinity you are talking about with the rays is an uncountable infinity, the infinity of the continuum. That infinity is larger.