Question 58
One day, one alien has come to the Earth. Every day, each alien does one of four things, each with a probability of one-fourth: (1) destroying himself, (2) splitting into two aliens, (3) splitting into three aliens, and (4) doing nothing. (A newly created alien also does one of these four things every day starting on the next day, but different aliens do not necessarily do the same thing and act independently.) Find the probability that there is eventually no alien on the Earth.