I believe it is a well known problem, but I couldn't find the solution.
In a vessel at hour 0 there is a 1 million bacteria. Every hour every bacteria produces two new bacteria and dies.
Right after that one half of all bacteria in the vessel is killed by random (i.e. 1 million times one bacteria is chosen uniformly from the vessel and killed). So now we have again 1 million left.
The process is repeated every hour on and on.
It intuitively seems to me that after enough repetitions all the bacteria in the vessel will be descendants of just one bacteria from hour 0.
Can this be proven?
Does it not always work like this: if we take a group of organisms of some species, after some (long enough) time, only the descendants of just one organism (or in sexual reproduction two: mother and father organisms) will remain?
For example, all living humans are descendants of just one man (biological Adam), who lived about 300 thousand years ago.
This means that no living human is a descendant (i.e. patrilineal) of another man who lived at the same time as biological Adam and was not his son/father (grand).
Does the fact that all humans are descendants of just one man comes from the probability theory and can it be strictly proven, i.e. can the probability be calculated?
