A colony of rare spherical cocci bacteria lives deep under lunar ice. After thousands of years of slowly reproducing (a process that often results in abject failure and death) in this harsh climate, only one lonely bacteria named John remains.
Suppose that the probability of an individual bacteria dividing successfully into two bacteria is 3/4, and that a bacteria must attempt the division process within two months of its immediately prior division experience.
John's time is up. It is time for him to attempt a division. What is the probability that poor John will be the proud predecessor of never-ending successive generations of his bacterial species?