For individual survival chances well below half, all colonies will frequently die out in finite time.
For high survival chances, many colonies will still die out, but the most successful will grow exponentially, and total population rises as a result.
Larger samples will show more outlier survivors. At short time scales, chance dominates the fate of each colony.
Generalizations of the problem can involve the possibility of more than one daughter cell at each generation, or a link between survival probability and existing population level (to model resource depletion, for example).
The problem can also be thought of as modeling the consequences of a series of double or nothing bets—note how much of the eventual "population" belongs to the most successful colonies.
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