  Let $G$ be any connected graph on $n$ vertices, $n \ge 2.$ Let $k$ be any
positive integer. Suppose that a fire breaks out at some vertex of $G.$ Then,
in each turn firefighters can protect at most $k$ vertices of $G$ not yet on
fire; Next the fire spreads to all unprotected neighbours. The $k$-surviving
rate of G, denoted by $\rho_k(G),$ is the expected fraction of vertices that
can be saved from the fire, provided that the starting vertex is chosen
uniformly at random.
  In this note, it is shown that for any planar graph $G$ with average degree
$4\frac{1}{2} - \epsilon,$ where $\epsilon \in (0, 1],$ we have $\rho_2(G) \ge
\frac{2}{9}\epsilon$. In particular, the result implies a significant
improvement of the bound for 2-surviving rate for triangle-free planar graphs
(Esperet, van den Heuvel, Maffray and Sipma, 2013) and for planar graphs
without 4-cycles (Kong, Wang, Zhang, 2012). The proof is done using the
separator theorem for planar graphs.
  This paper is the corrected version of (Gordinowicz, 2018) unified with the
corrigendum.
