The growth dynamics of pollen cells can be modeled by binary splitting as follows: After one unit of time, a cell either splits into two or dies. The new cells develop according to the same law independently of each other. The probabilities of dying and splitting are 0.46 and 0.54, respectively.
(a) Determine the maximal initial size of the population in order for the probability of extinction to be at least 0.3.
(b) What is the probability that the population is extinct after two gener- ations if the initial population is the maximal number obtained in (a)?