Why does an infinite universe imply that everything that can happen will happen? Why can’t an infinite universe be boring and uneventful?
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Simple probability.
Let’s say that we are throwing a fair coin, it has a *50/50* chance of landing on either tails(T) or heads(H), and we want it to land on **heads at least once.**
With 1 throw you have two possible outcomes – T or H, so the chance to get it is 50% (1 of 2).
With 2 consecutive throws, you have 4 possible results – TT, HH, TH, and HT, your chances of scoring rise to 75%(3 of 4).
With 3 throws we have 8 possible results – TTT, TTH, THT, HTT, HHH, HHT, HTH, THH, which means 87.5% of scoring(7/8).
And so on. The closer your number of throws is to infinity the closer your chance of scoring is to 100%, culminating at guaranteed if you perform infinitely many throws because even if you did X out of infinity throws without getting your desired result you will still have an X+1 throw that can still result with what you expect.
The same logic can be applied to our universe – if we cut a box of space of some size and define the specific spatial combination of atoms inside of that box as “something happening” then it’s pretty unlikely that any other randomly taken box of that size from any other place in the universe will be the exact “something” we are looking for, but the more boxes you cut and check the more likely you are that at least one of them has an exact same combination of atoms inside and in an infinite universe you can cut an infinite amount of such boxes, meaning that as long as a given “something” has a non-zero chance of happening you will eventually arrive at a box where it happened because even if you did X boxes where it didn’t the next X+1 box might be the one where it does, thus “everything that can happen will happen”.
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