Suppose a single cell microbe can replicate into two cells during replication event. The probability that a cell is still alive until this event is given by $x$. Suppose we start with one single cell microbe on a plate. What is the probability that these microbes will eventually go extinct on the plate? What is the average generation time (number of replication events) to reach extinction?
I thought this was a simple geometric distribution problem. But I got really stuck right now.