What is the typical life of a carbon atom? What I mean by this question: 
Carbon is the basis of life on Earth. Life started several billion years ago and I suppose that the majority of carbon atoms was already on Earth back then. 
If I take a single Carbon atom from my body and could reconstruct its history, what would that history include? For example, is it probable that it had been incorporated in another human?
Has anyone ever come across such estimates/probabilistic calculations?
 A: Earth contains about $7.30\times 10^{-7}$ carbon by weight, or $4.36\times 10^{18}$ kg of carbon in total. The biosphere contains about $5\times 10^{14}$ kg above ground, soil holds about $1.5\times 10^{15}$ kg, the atmosphere $7.3\times 10^{14}$ kg, and the oceans $3.8\times 10^{16}$ kg. 
That means that if you pick a carbon atom at random it will be deep in the planet with 99.07% probability. If we pick an atom at random that isn't part of a rock there is 1.2% chance that it is in a living organism (or, actually, most likely part of dead wood), 3.7% chance that it is in soil, 1.8% chance that it is in the atmosphere and 93% chance that it is dissolved in the ocean. 
But this is the momentary distribution. Atoms move between these reservoirs at different rates. Mantle diamonds remain for billions of years while a carbon atom in a living organism is going to escape within a typical time-span of days to years. The carbon cycle sets these rates, which have changed over Earth's history a fair bit. Before photosynthesis carbon got removed from the atmosphere mainly by weathering of silicates and the burial of carbonate rocks by continental subduction, before being recycled back through volcanic eruptions. In this case an atom may have resided in the atmosphere for a few centuries, then spent hundreds of millions of years in a sedimentary rock. With photosynthesis there is much more bouncing back and forth between the atmosphere, biosphere and ocean with occasional slow detours through rock. The average residence time of carbon in the atmosphere is 5 years, in vegetation 10 years, soils around 25, 380 years in oceans, and millions of years in rock. 
Humanity contains in total somewhere around $9.5\times 10^{10}$ kg carbon, about 0.02% of the total biosphere (which is pretty impressive for a single species). So a carbon atom bouncing around outside the rocks has a probability at any given time of $P=2.3\times 10^{-6}$ to be in a human. So if you look at the history of an atom and assume that over the past million years it has only hung around in living beings, switching host every 10 years, the probability that it managed to avoid being part of another human would be $(1-P)^{10^6/10}=79$% - much of your carbon has likely never been in a human (but, since there are so many carbon atoms, you will contain a vast number of reused atoms - this is a classic estimation example). 
Since the above calculation naively assumed the current large humanity rather than the much smaller ancestral population, it is likely an underestimate. And clearly we should not assume atoms spending all their time in the biosphere. To do this calculation properly we should run this as a continuous time Markov chain model where the transition rates between different reservoirs correspond to carbon fluxes. 
To sum up these estimates, a particular carbon atom you meet will likely have spent most of its time buried deep in the earth, with this often being its first foray into the surface world. It has spent the last few centuries or millennia mostly in the ocean, with occasional dances into the atmosphere and biosphere only to return to the sea. It may have been part of a human, but it is more likely this is the first time. 
