Ufyukyu

0 $begingroup$ I am considering a standard extinction problem, that is: A bacterial colony consists of individual bacteria. One of the following happens with each bacterium each second: The bacterium dies. The bacterium remains without a change. The bacterium splits in two bacteria. The bacterium splits in three bacteria. Each of the above happens with equal probability $frac{1}{4}$ . Estimate probability that the colony that initially consist of one bacterium will never die. There is a well documented approach for solving this, e.g. https://www.math.ucdavis.edu/~gravner/MAT135B/materials/ch14.pdf, http://math.uchicago.edu/~may/REU2015/REUPapers/Csernica.pdf. This approach is working with probability that the colony has died by timestep $n$ . However there is a slightly variant of this approach t