  The tunneling rate, with exact prefactor, is calculated to first order in
\hbar for a closed FRW universe filled with perfect fluid violating the strong
energy condition. The calculations are performed by applying the
dilute-instanton approximation on the corresponding Duru-Kleinert path
integral. It is shown that a closed FRW universe filled with a perfect fluid
with small violation of strong energy condition is more probable to tunnel than
the same universe with large violation of strong energy condition.
