re: Please answer the following math/philosophy question

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The deal with evolution though is that you can't accurately figure out the probability of life being created, because we don't know how long "matter" has existed for there to have been a probability value assigned to it being able to transform into a life form via specific chemical reactions.

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Right. No one knows the calculus of such a problem.

But if you acknowledge that it equates to a non zero probability then you have to conclude that the longer the time line goes on, the greater chance of this occurring.

I don't think this is true.

I remember getting nailed in statistics class for shite like this.

If something has a 25% chance of occurring once, then doesn't, it still has a 25% chance the next attempt. Previous failure doesn't affect future chances.

Sure, longer time goes on, you have more attempts, but it still doesn't make something "bound" to happen unless you have an infinite amount of time, which our universe does not (entropy/heat death)

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If something has a 25% chance of occurring once, then doesn't, it still has a 25% chance the next attempt. Previous failure doesn't affect future chances.

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You would be partially correct. If you flip a simple coin the previous outcomes don't have an influence on the next outcome.

But if you were to flip a coin 9 times, the probability of you hitting tails one time out of any of those 9 times certainly isn't 50% Only the individual attempts are 50%

With the passage of time you could essentially look at it as repeated attempts.

You're referring to the Monte Carlo fallacy, which is a little different. The MC fallacy pertains to the probability of an event happening as one step in a causal chain rather than the entire chain.

Going back to the nomenclature I used earlier -- Event X with Y probability and Z attempts -- we can see that as Z increases, the chances of X happening go up. But there are two things that fuel the chance of X happening: Y probability, and Z attempts. It's not fallacious to say that as Z increases, the chance of X happening increases. Where it is fallacious, and where the MC fallacy comes into play, would be if you argued that as Z increases, Y also increases. Y stays the same, the chance of X happening just goes up (and eventually reaches 1) because of Z going up.

Does that make sense?

EDIT: Just thought of an example that fits. You would agree that I have a better chance of flipping a coin and getting heads if I got to flip the coin 10 times instead of 1. But that's because I got 9 more tries. We would have a problem if I said that because I didn't get heads before, my odds of getting heads go up to 60% or 70% or whatever have you. The former (my chances improving because of more attempts) is just basic logic, the latter (the odds themselves changing because I failed previously) is the MC fallacy.

Gotcha. Probability is weird (and considering infinity with it just makes it even weirder), gotta agree there

What is the answer of this math/philosophy question supposed to answer? Without knowing to what the question is referring to, yes, all events with non-zero probabilities will occur given enough time.

Could life have begun simply by random combinations of atoms given infinite attempts? Sure

Could humans have evolved from the simplest organisms into what we are today given enough time? You bet

But this logic can't be applied to the creation of the universe, as time, space and matter had yet to exist prior to the big bang.