Amoeba Extinction
An amoeba each minute either dies, stays the same, splits into two, or splits into three, each with probability 1/4. Offspring behave independently and identically. What is the probability the population eventually dies out? Give an exact expression or a decimal rounded to 3 decimal places.
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Source: Standard Galton-Watson branching-process extinction problem, after Francis Galton and Henry William Watson (1875). Statement written for AxiomIQ.