Assignment:
A single amoeba is in a pond. Each day, each amoeba present in the pond will die with probability p, will split into two live amoebas with probability q, and will stay alive but not split with probability 1 - p - q.
(a) Describe a probability space for this experiment as well as you can.
(b) Find the probability that after two days there are no amoebas in the pond.
(c) What is the probability that there will always be amoebas in this pond?
Provide complete and step by step solution for the question and show calculations and use formulas.