Consider a single amoeba that at each time slot splits into two with probability $p$ or dies otherwise with probability $1-p$. This process is repeated independently infinitely at each time slot, i.e. if there are any amoebas left at time slot $t$, then they all split independently into two amoebas with probability $p$ or die with probability $1-p$. Which of the following is the expression for the probability that the race of amoeba becomes extinct.
- $\min \left\{\frac{1 \pm \sqrt{1-4 p(1-p)}}{2 p}\right\}$
- $\min \left\{\frac{1 \pm \sqrt{1+4 p}}{2 p}\right\}$
- $\min \left\{\frac{-1 \pm \sqrt{1+4 p(1-p)}}{2 p}\right\}$
- $\min \left\{\frac{1 \pm \sqrt{1-4 p(1-p)}}{2(1-p)}\right\}$
- None of the above