A very qualitative way to look at it:
- The Earth, and therefore you are formed of the same material that contributes to the metallicity of our Sun
- Our Sun is a population I star, which means that it has a relatively high metallicity indicative of having formed after the heavy and short lived stars of population II had already had their big blow offs.
- The population II stars divide into early and late groups, and all post-date the assumed population III stars.
From this I conclude that a non-trivial number of the nucleons in your body have been part of a few stars. Maybe as many as five. As Georg notes there has been time for the most prolific path to include many stars (dozens?).
Certainly all the carbon, nitrogen, oxygen and trace elements that make up your body have been part of at least one star.
None of these facts shed much light on the average star-membership-history of the nucleons that make up your body.
Supernovae do occur all the time, if you are thinking on cosmic time scales. The number I have typically seen in the Milky Way is that supernova occur once per century, roughly. Maybe a little bit more often, maybe a little bit less. Relative to a the lifetime of a typical star, that is a very short timescale indeed.
Now, the relevant number of stars is not actually 400 billion. There are two basic ways of producing a supernova. One is with a very massive star. Massive stars, meaning stars at least about 10 times as massive as the Sun, are quite rare, relative to stars like the Sun and more low mass stars. The other is when a white dwarf experiences some sort of mass transfer (the details of which are still not understood) from another star, exceeds its maximum mass, and explodes. While binary star systems are quite common, not all binary stars are close enough that sufficient mass will be transferred from one star to the other.
You are correct that stars are dying all of the time, much more frequently than supernova are observed. The key is that when stars like our Sun die, they do not produce supernova.
One other thing worth noting is that we do not necessarily see all supernova. This seems on, on the face of it, ridiculous. Supernovae are extremely bright! However, since very massive stars produce supernovae, and also have very short lifetimes, some supernovae may be hidden because they occur while still surrounded by the remnants of the molecular cloud from which they formed. With more and more advanced telescopes, the likelihood of completely missing a supernova in the Milky Way now is pretty low, but there have been supernovae in the Milky Way in the past 400 years since SN 1604 that were not visible to the naked eye as a result of being blocked out by dust. The best known example is Cassiopeia A, which from its supernova remnant is known to have occurred in the mid to late 1600s, but was not recognized at the time. Looking around some more, it appears that another young supernova remnant has recently been identified (Youngest Stellar Explosion in our Galaxy Discovered) that was not seen by the naked eye.
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The estimates I've read are similar to yours: 200 to 400 billion stars. Counting the stars in the galaxy is inherently difficult because, well, we can't see all of them.
We don't really count the stars, though. That would take ages: instead we measure the orbit of the stars we can see. By doing this, we find the angular velocity of the stars and can determine the mass of the Milky Way.
But the mass isn't all stars. It's also dust, gas, planets, Volvos, and most overwhelmingly: dark matter. By observing the angular momentum and density of stars in other galaxies, we can estimate just how much of our own galaxy's mass is dark matter. That number is close to 90%. So we subtract that away from the mass, and the rest is stars (other objects are more-or-less insignificant at this level).
The mass alone doesn't give us a count though. We have to know about how much each star weighs, and that varies a lot. So we have to class different types of stars, and figure out how many of each are around us. We can extrapolate that number and turn the mass into the number of stars.
Obviously, there's a lot of error in this method: it's hard to measure the orbit of stars around the galactic center because they move really, really slowly. So we don't know exactly how much the Milky Way weighs, and figuring out how much of that is dark matter is even worse. We can't even see dark matter, and we don't really understand it either. Extrapolating the concentrations of different classes of stars is inexact, and at best we can look at other galaxies to confirm that the far side of the Milky Way is probably the same as this one. Multiply all those inaccuracies together and you get a range on the order of 200 billion.