Ah, part of this I agree with. The first half.

The odds of rolling a particular number are 1/6 (excluding the unlikely event of a cocked die).

The odds of rolling that same number on a subsequent roll are again 1/6.

The odds of rolling the same number twice in a row are 1/36.

This second result is exactly equivalent to a pair of dice and any combination.

So let's take a dodecahedron die from a D&D game. Each side has exactly the same probability of selection = 1/12. Getting the same number a second time is still 1/12 but the combined probability of getting the same number in any two rolls is 1/12 * 1/12 = 1/144.

If we had 5 dodecahedrons the combined probability would be a simple extension of that multiplication.

So now let's go to lottery balls. Assume there are 500 balls placed in bins of 100, each ball then numbered 1-100.

Each ball in each separate bin has an equiprobable chance of being pulled = 1/100.

So what is the chance of pulling say 55 from bin 1? = 1/100.

What is the chance of pulling 55 from Bin 2? = 1/100.

Etc.

What is the combined probability of drawing 55 from each bin?

1/100 * 1/100 * 1/100 * 1/100 * 1/100 = 1/10,000,000,000

Pulling a ball from Bin 1 does not affect the probability of pulling any number from Bin 2, Bin 3, etc. This is exactly equivalent to the coin toss and die toss.

B