If mitochondria exist at random within a cell, isn't there a possibility that cell division will result in a daughter cell with no mitochondria? If not, what is the process for guaranteeing at least one is present in each daughter cell? If so, what happens to that cell?
Isn't there a possibility that cell division will result in a daughter cell with no mitochondria?
Yes, there is always the possibility. However, there must be a strong negative selection pressure against eukaryotic life that cannot achieve the proper partitioning of mitochondria, so you can imagine that there are mechanisms in place to prevent this case.
Mitochondria are both passively and actively partitioned to daughter cells. This is understood to occur through the cytoskeleton and with the control of mitochondrial fusion and fission at key stages of the cell cycle, prior to mitosis and cytokinesis!
In addition to S Pr's excellent example, I wanted to point out that some very recent research describes some special behavior in oocyte development specifically related to mitochondria selection.
Here's a easy-to-read version: https://www.sciencedaily.com/releases/2019/05/190515131741.htm
Here's the original version in Nature: https://www.nature.com/articles/s41586-019-1213-4
Specifically, during meiosis, the oocyte specifically "puts the mitochondria to the test" by separating all of them (fragmentation) and having each of them operate independently. (Typically mitochondria act in concert, each one potentially making up for deficiencies in their peers). Any that do not "make the cut" are eliminated, and the result is an egg cell that has the best mitochondria to pass along to the next generation.
A typical animal cell has 1000-2000 mitochondria. From a statistical point of view, assuming a random distribution of the mitochondria and that the cell splits in half, the probability of having 0 mitochondria is (1/2)^1000 or 9e-302. This makes it an impossibility for all practical purposes.
With enough mitochondria, a process to ensure the cell splits roughly in half and a somewhat random distribution of mitochondria would be sufficient to get at least one mitochondria in each daughter cell.
To address the assumptions:
- Random distribution of mitochondria - assumed in the question
- Cells split roughly in half - source on dividing assymetries "In somatic divisions, however, cell size asymmetry is mild and, only rarely, one daughter cell is more than double the size of the other."