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I would like to know, from a mathematical point of view what is the probability that

1) There is organic life on other planets 2) There are advanced species like us or even greater than us on other planets?

Is there a formula or equation or a way we can calculate this probability?

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The probabilites are unknown at the moment (March 2014), since there is only one known planet (Earth) harboring life. This doesn't allow any meaningful probability estimates for the occurence of life, based on empirical data.

The overall formation of life is too complex to allow simulations based on current technology. Although some intermediate steps can be simulated or performed by experiment, e.g. by the Miller-Urey experiment.

The Drake equation is a simplified attempt to decompose the probability into factors. Some of the factors aren't known yet. But there has been much progress in estimating the frequency of exoplanets, and the probability of planets to be habitable. From this news release one could estimate (order of magnitude), that there is one habitable planet around a Sun-like star per about 1,700 (about 12³) cubic light years in our region of the Milky Way ("... the nearest sun-like star with an Earth-size planet in its habitable zone is probably only 12 light years away...").

We don't know the probability for habitable planets to develop life, nor to be colonized. Probabilities of complex life forms are even more difficult to estimate (yet). More discussion about habitability of exoplanets on Wikipedia.

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Thanks Gerald I have greatly enjoyed reading on the Milley-Ulrey experiment and the Drake equation. While the former experiment proves that a habitable planet will mostly likely develop life the odds of that life becoming intelligent enough to colonize seem quite low as is evidenced by our planet. But then there are uncountable galaxies in the observable universe so a low non zero probability of planets with intelligent life could still translate to many intelligent life forms out there. –  nemesis22 Mar 19 at 16:11
    
@nemesis22 That's plausible; may be there are billions of intelligent life forms in the observable universe, but it's hard to prove. –  Gerald Mar 19 at 18:07
    
One observation, yes, and that one is statistically invalid since we are the observer observing ourselves. Our existance is exactly as likely in a universe where we are alone as in a universe where we have company: 100%. –  LocalFluff Mar 20 at 9:34
    
Drakes equation should take relativity into account... It'll significantly reduce the chances for life existing elsewhere; as seen by us. –  frodeborli Sep 1 at 18:52

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