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I was wondering if you had some simple procedure, like say rolling a six sided die, and said you did this an infinite amount of times, would it be valid to say eventually you will roll a 6? Of course this is an ideal situation where each side has an equal chance of being rolled.

I'm wondering if it is accurate to say you will eventually have any outcome occur (assuming it is possible on any individual trial, no matter how unlikely)

Is this even valid considering its not really possible to actually have this happen in real life?

Also just for fun, what about an example taken to the extreme like an infinite amount of monkies all writing on typewriters, assuming they at least type something will at least one type a Shakespeare play exactly? Will an infinite amount type a Shakespeare play?

Thank you.