Question: U ' 5. Let 0 5. Let 0 < p < 1. Consider a branching process with two types of individuals: type A and type

U ' 5. Let 0

5. Let 0 < p < 1. Consider a branching process with two types of individuals: type A and type B. Each type A individual has exactly two offsprings. The type of each offspring is chosen randomly and independently of all the other choices: it will be of type A with probability p and of type B with probability 1 p. Type B individuals have no offsprings. Suppose that the process starts with a single type A individual. Find the probability that this population eventually goes extinct. Hint: Consider the process of just one of the types.

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