Math Adventures/How many grandparents?

It is likely you have 2 parents, 4 grandparents, and 8 great grandparents.

Continuing that pattern, how many gggggggggggggggggggggggggggggggggggg…great grandparents do you have from 40 generations ago?

What is the average lifespan of a generation, measured in years?

How many years ago did your 40th generation grandparents live?

What Calander year was that? What is a reasonable estimate of the world population at that time?

What is the probability that someone, chosen at random today, shares some relative of yours that was living at that time?