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Is there a difference between answering the questions:

  1. What is the probability that a population goes extinct?

  2. What is the probability that a population eventually goes extinct?

For example, let $p_i$ be the probability that a parent has $i$ children,

$ \ \ p_0=0.5$, $ \ \ p_1=0.25$, $ \ \ p_2=0.25$

Then, is the answer for question one, simply $0.5$, and is the answer for question two $1$ (found by solving $h(z)=z$, where $h(z)$ is a probability generating function and $z$ is the probability of eventually going extinct)? Or should the answer for both questions be $1$?

sucksatmath
  • 877
  • A population either goes extinct or it doesn't. There is no middle way. The "eventually" could perhaps imply that the population first grows and then ultimately goes extinct. Nonetheless, I don't see a difference in the 2 questions. – imranfat Nov 25 '17 at 20:44
  • The first question is a little ambiguous, but if I saw that question the first thing I would guess it means is the second question. – Qiaochu Yuan Nov 25 '17 at 20:59
  • Me too: I agree with Qiaochu Yuan – kimchi lover Nov 25 '17 at 21:23

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