Final answer:
In both mitosis and meiosis, cells undergo one round of DNA replication before cell division and utilize spindle fibers during metaphase and anaphase to separate sister chromatids, resulting in the proper distribution of chromosomes.
Step-by-step explanation:
Two events common to both mitosis and meiosis that ensure the resulting daughter cells inherit the appropriate number of chromosomes are the one round of DNA replication that occurs before each process and the separation of duplicated chromosomes through the actions of the cell's spindle apparatus.
During the S-phase of the cell cycle, one cycle of DNA replication occurs, resulting in chromosomes with two sister chromatids. This replication is crucial as it equips the cell with a duplicate set of DNA for distribution to the daughter cells. In mitosis, this leads to two diploid daughter cells that are genetically identical to the parent cell. In meiosis, despite starting with the same replication event, two rounds of division occur, producing four haploid cells, each genetically distinct.
The separation of chromosomes is another shared event. In both mitosis and meiosis, spindle fibers attach to chromosomes and pull apart the sister chromatids during later phases (Metaphase and Anaphase). This ensures the accurate distribution of chromosomes to daughter cells. In mitosis, each new cell receives a complete set of sister chromatids, while in meiosis, the process eventually leads to daughter cells with half the number of chromosomes.