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Say we have the following problem (source):

Bobo the amoeba has a 25%, 25%, and 50% chance of producing 0, 1, or 2 offspring, respectively. Each of Bobo’s descendants also have the same probabilities. What is the probability that Bobo’s lineage dies out?

You can probably the probability of extinction $p$ as $$p = \frac{1}{2}p^2 + \frac{1}{4}p + \frac{1}{4}$$

Which if you solve leads to solutions 1 and .5. That said, why is the "correct" answer 1/2?

There is a discussion of a similar problem on some of the comments on this thread (Amoeba Interview Question), but I don't really understand the reasoning, especially since in this problem we don't have a root above the value of 1.

Thoughts?

zthomas.nc
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  • Looks like you are missing the self-study tag. – StatsStudent Jan 27 '19 at 22:22
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    There is maybe a typo in your equation. It is + 1/4 instead of - 3/4 – Sextus Empiricus Jan 27 '19 at 22:33
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    If you equate the probability to get extinct like that $$\text {probability to die = probability off spring dies}$$ then $1$ should always be one of the solutions. It is a vacuous truth. – Sextus Empiricus Jan 27 '19 at 22:45
  • Agree, $p = \frac{1}{4} + \frac{1}{4}p + \frac{1}{2}p^2$ does solve for $\frac{1}{2}$ as you expected. How are you getting $-\frac{3}{4}$? – runr Jan 27 '19 at 22:47
  • https://stats.stackexchange.com/a/4769/919 (an answer to the duplicate) explains how to determine whether $1$ is worth considering as a possible answer. – whuber Jan 27 '19 at 23:10
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    @whuber To be fair, the OP listed this same link to the "duplicate" in his question with the idea of discussing the reasoning which he didn't fully understood. Sending him to the same link and closing the question seems very bold. – runr Jan 27 '19 at 23:43
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    @zthomas.nc I have added an answer to the duplicate question that might help you a bit more. – Sextus Empiricus Jan 28 '19 at 11:10
  • @Nutle Bold it is not: this is standard SE policy. Moreover, in a comment I explained specifically how that thread answers every aspect of the present question. – whuber Jan 28 '19 at 13:46
  • @whuber I presumed OP was looking for either a correction (as in Martijn's comment), or, at best, something in the lines of "explain like im five" answer on top of the currently available ones in the link. But I see they corrected the equation without removing the question, suggesting the latter. – runr Jan 28 '19 at 15:18
  • @whuber I can't argue, of course, if this is a standard SE policy. My initial comment just resonated with one of the questions in StackOverflow's 2019 Survey, with one of the question focused on "feeling of being welcome in the community". I do have a feeling that if OP commented under one of the answers asking for ELI5 explanation, or "why am I getting these <..> probabilities", the response would be to post a new question, since the original question was already answered. (at least I've seen a fair share of such responses) – runr Jan 28 '19 at 15:27

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