Are cells guaranteed to get at least one mitochondrion when they divide? 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!

Here is a great review from several years ago that addresses your question well.