Question

how do mitochondria produce their own protein

Answer 1

Although the mitochondrial genome encodes some of the proteins in the mitochondrion, more than 90% of the proteins in the mitochondrion are encoded by genes in the cell's nucleus.

These nuclear genes are transcribed and translated by the cellular machinery to make proteins in the cytoplasm.

Hope this helps you.

Answer 2

mitochondria produce their own protein because the have their own DNA