Amoeba Population Extinction - Quant Trader Interview Question
Difficulty: Hard
Category: Conditional Probability
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Topics: probability, recursion, fixed-point, branching-process
Problem Description
A single amoeba exists in a petri dish. Every minute, one of three things happens:
- With probability 25%, the amoeba dies.
- With probability 25%, the amoeba remains unchanged.
- With probability 50%, the amoeba splits into two identical amoebas.
Assuming these events are independent across time and amoebas, what is the probability that the amoeba population will eventually become extinct (i.e., there are zero amoebas remaining)?
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