Is it mathematically impossible for us to be the only planet with life?

If another planet similar to earth exists, wherein it has exactly the same size and composition as earth and it resides at a similar distance to its sun, as earth resides to its own sun, would such a planet be guaranteed to host life and would that life be necessarily similar to life on earth?

• If the answer is yes, wouldn't the fact that space is so large, then, virtually guarantee that such a planet, with life, exists?

• Answer:

  1) We don't know, although it seems that life seems to naturally from, once conditions are right 2) Unlikely.  Even if the biochemical processes are similar, there are so many "random" events in evolution that it's unlikely that the life would look similar to our own.  Also, there are some odd things that have happened in our own planet, such as the Cambrian explosion.  We don't know if this is something that usually happens once you have life, or if something highly improbable happened. 3) Also there are some things about earth that are odd.  The big one is that the moon exists.  Apparently the earth was hit by a mars sized body that created the moon.  If the collision was slightly different the earth might have been totally destroyed or else you would have had a total miss with no moon.