Amoeba population | PuzzledQuant

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A small pond has a single amoeba living inside it. This particular amoeba has a unique ability, where every minute it can either die, stay alive, split into two, or split into three, each with an equal probability. The offspring produced by this amoeba will also have the same behavior, and will act independently of other amoebas. What is the likelihood that this amoeba population will eventually die out?