Imagine an isolated population in which each adult female has a distinct mitochondrial genome. In each generation, every adult female has two children (with a 50% chance of being male or female). After each generation, we will assume that all the adults die out, and all the children become adults.

After seven generations, what is the expected percentage of mitochondria from the original population of females that will still exist in the population’s children? Express your answer as a decimal between 0 and 1, rounded to three decimal places.

Note: after one generation, there will be 100% of the mitochondria from the original population present in the population’s children since male children receive the mitochondria from their mothers (but do not pass them on to their own children.)