Each minute an amoeba dies, stays, splits in two or splits in three. Will the family die out?

A single amoeba, and each minute every amoeba independently dies, stays, becomes two or becomes three, each with probability 1/4. The story asks the probability the population eventually dies out. You type your answer and check it. Then you step through the answer and the breakdown.

Why quant interviews test this

This tests first-step analysis on a process that renews itself, and knowing why p = 1 is the wrong root. The written solution is at /brain-teasers/amoeba-population/solution.

The The Amoeba Population guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

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