re: Please answer the following math/philosophy question

quote:

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There are essentially 2 variables

1. A time line that is infinite

2. Events that are unlikely to happen often but have a non zero probability of occurrence

Is it true that all events with a non zero probability will eventually occur given an infinite amount of time?

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When I first read this, the easy answer is yes, everything will happen at some point. Then I tried to think of a way to disprove it, and now I can. The problem with your question is, like most academics, you are assuming a vacuum. Here's an example of a non zero probability event that can never come true. Think back to the days of the dinosaurs, and what's the probability that one of them would watch the Saints win the Super Bowl? First you have to assign the probability that at some point humans would come along. Then what's the probability that one of those humans would invent the game of football, etc, etc, etc. The probability of all of those thing must be non-zero, because they happened. But you also must factor in the probability of dinosaurs becoming extinct before the Saints win the Super Bowl.

If you have 2 non-zero probabilities that conflict each other, then time not longer becomes the problem, outside factors also need to be considered.