Branching process extinction (supercritical)

HardProbability Stochastic Processes~6m

Each individual has $0$ offspring with probability $1/4$ and $2$ offspring with probability $3/4$ . Starting from one individual, what is the extinction probability? (to 3 decimals)

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Set $q$ equal to the offspring generating function evaluated at $q$ .
Factor $3q^2 - 4q + 1$ and take the smaller root.

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0.3333 (± 0.005)

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Branching process extinction (supercritical)

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