Mitochondria divide just like other cells (they even have their own DNA). Presumably, the mitochondria already replicated a few times inside the host cell, so when the host cell split, both daughter cells had mitochondria too. Think of it like adding a raisin (the mitochondria) to a ball of dough (the host cell). The raisin multiplied and distributed around the dough, and then the dough ball got split in half with raisins now in both halves.
Cells typically have many, many mitochondria in them. This is similar to other endosymbiotic things, like algae symbionts (zooxanthellae) in corals. Coral cells host zooxanthellae and when they split, zooxanthellae can be transferred to both daughter cells. Zooxanthellae reproduce independently of host cells, but hosts can influence this reproduction rate and can also expel zooxanthellae if stressed (this causes coral bleaching). Zooxanthellae can spread between cells and between corals if conditions are right, so they aren’t only transferred by cell division.
Something similar likely happened with mitochondria early on. Bacterial relatives of mitochondria (Rickettsia) are intracellular parasites that live and multiply within cells and spread between them too. Probably you had a similar endosymbiotic bacteria that was usually beneficial rather than harmful to the host, so being carried along to daughter cells benefitted both, and over time the association grew closer and became regulated more tightly.
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