Species evolution - Lycée Emmanuel d'Alzon (Nîmes)

We consider a species whose reproductive probabilities are known. We assume the following probabilities:
\begin{itemize}
\item Probability of having $0$ offspring: $p_0$;
\item Probability of having 1 offspring: $p_1$;
\item Probability of having 2 offspring: $p_2$;
\item Probability of having 3 offspring: $p_3$;
\item Probability of having 4 offspring: $p_4$;
\end{itemize}
and we assume that the number of births is independent in each generation.

What is the probability that the species will become extinct?