  There are $n$ independent Bernoulli random variables $I_{k}$ with parameters
$p_{k}$ that are observed sequentially. We consider a generalization of the
Last-Success-Problem considering $w_{k}$ positive payments if the player
successfully predicts that the last "1" occurs in the variable $I_{k}$. We
establish the optimal strategy and the expected profit in similar terms to the
Odds-Theorem. The proof provided here is an alternative proof to the one Bruss
provides in his Odds-Theorem (case $w_{i}=1$) that is even simpler and more
elementary than his proof.
