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?

Solution Preview

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a.) A probability space is a measure space such that the measure of the whole space is equal to 1. In other words, a probability space is a triple consisting of a set (called the sample space), a σ-algebra (called also σ-field) of subsets of (these subsets are called events), and a measure on such that (called the probability measure). The sample space for this experiment is (please see the attached file) = {(p),(q),(1 - p - q)} in that there are 3 possible outcomes; the amoeba will either die, live, or produce another amoeba. The of subsets for ...

Solution Summary

In this solution, a probability space (amoeba in a pond) is fully assessed.

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