# Conditional Probability and the Fermi Paradox

Certainly most of you have stared into the skies and wondered if somewhere light-years away some form of life is doing what you are doing (or maybe they’re narcissistic enough to not care whether there’s another intelligent life form out there). Well, the thing is, most people suggest that there’s a very high probability, as might be calculated from their inputs into the Drake equation, for life to exist elsewhere in the universe. And yet…we still have not found any. Why? The universe was miraculous enough to bring us to life, so why would the similar occasion not happen in many places in the universe?

I believe the best way to communicate my opinion is through conditional probability. First, an analogy. Suppose there’s a rare but serious disease that 0.01% of the population has. There happens to be a test developed for the disease that is incredibly accurate—in fact, is has a 99% chance of reporting the correct result given a particular patient; if they have the disease, there’s only a 1% chance that this hypothetical test fails to detect this disease. If they don’t, there’s only that 1% chance that the patient should end up being falsely alarmed by the test. Sounds like a good test right?

So you go to take the test…and it reports that you have tested positive for the disease. You are in shock. What has just happened? Can you only hope for that 1% chance that the test is wrong?

Thankfully, yes. Because the chance that you do not have the disease is in fact not 1%. Take into account all possibilities that could be happening: either you have the disease and test positive or you don’t have the disease and test positive. You have the disease and test positive with a 0.0001(0.99)=0.0099=0.99% probability. You don’t have the disease and test positive with a 0.9999(1-0.99)=0.9999(0.01)=0.009999=0.9999% probability. You actually have a higher probability of not having the disease than having it by that small sliver of a percentage (50.2488%). Although if this is truly a serious disease, even 50% might not be that great to learn about, but it certainly is many times greater than that 1% chance. This is the thing about conditional probability; specific information can narrow possibilities down substantially and thus make probabilities different from what may be intuitively expected; in this case, one has to realize that the 1% of the population occupies (only) 50% of the positive test.

But surely conditional probability isn’t messing with the existence of another civilization?

Not so. Remember how it seems like a miracle that there is life in a universe, and hence there should probably be other life? Well, what’s the probability the life exists in a universe? Small?

Well, let’s change that question a bit. What’s the probability that given a universe exists, life exists in it?

Wait, what has changed? Oh, potentially quite a bit. Because the probability that given a universe exists, life exists in it is…1.

Let’s consider the cases of life existing and life not existing and see what happens. What is the probability of a universe existing given that life does not exist in it?