First of all: the question needs to be qualified by what we mean by "out there". The galaxy? The observable universe? The entire universe?
The universe might be infinite, in which case: yes, there is life out there. We know the probably of life forming on any given planet must be greater than zero, or else we wouldn't be here. From this we can deduce the average volume which contains exactly one planet with life, which must be finite. Whether it makes sense to talk about what could be happening beyond the cosmological event horizon is another discussion.
If we are talking about the observable universe or an even smaller volume: How can you say it's statistically implausible without knowing the probability of life forming on any given planet? It might be incredibly small, yet greater than zero. Your line of reasoning is incredibly common but I can't help but feel like it's mainly driven by wishful thinking.
Probably extrapolating from the fact that life here on Earth being found in harsh conditions, and those conditions being likely to be found all over the universe.
The universe might be infinite, in which case: yes, there is life out there. We know the probably of life forming on any given planet must be greater than zero, or else we wouldn't be here. From this we can deduce the average volume which contains exactly one planet with life, which must be finite. Whether it makes sense to talk about what could be happening beyond the cosmological event horizon is another discussion.
If we are talking about the observable universe or an even smaller volume: How can you say it's statistically implausible without knowing the probability of life forming on any given planet? It might be incredibly small, yet greater than zero. Your line of reasoning is incredibly common but I can't help but feel like it's mainly driven by wishful thinking.