Single amoeba (a unicellular organism) lives in a pond. After one minute the amoeba will either die, split into two amoebas, or stay the same, with equal probability, and in subsequent minutes all living amoebas will behave the same way, independently. Let E denote the event that the amoeba population will eventually die out. We also define the following events:
F1 denotes the event that after the first minute, amoeba will die; F2 is the event that after the first minute, amoeba will split into two; F3 denotes the event that after the first minute, the amoeba will stay the same.
Find the conditional probabilities P (E|F1), P (E|F2), and P (E|F3) (possibly in terms of P (E)).

Question

05-06-2024
Mathematics

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Single amoeba (a unicellular organism) lives in a pond. After one minute the amoeba will either die, split into two amoebas, or stay the same, with equal probability, and in subsequent minutes all living amoebas will behave the same way, independently. Let E denote the event that the amoeba population will eventually die out. We also define the following events:
F1 denotes the event that after the first minute, amoeba will die; F2 is the event that after the first minute, amoeba will split into two; F3 denotes the event that after the first minute, the amoeba will stay the same.
Find the conditional probabilities P (E|F1), P (E|F2), and P (E|F3) (possibly in terms of P (E)).

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