Solution
= Solution
For $p>0$, equivalently $0\leq q<1$, the <geometric series> gives
$$
\boxed{\sum_{n=1}^{\infty}q^{n-1}p=\frac p{1-q}=1.}
$$
Thus <absorption probability> is one. The qualification matters: if $p=0$, the process alternates between $B$ and $I$ forever and never reaches $A$.