Rate from a mixed survival probability

The service times (in minutes) at two petrol pumps $P_1$ and $P_2$ follow distributions with probability density functions $f_1(x) = \lambda e^{-\lambda x}, \; x > 0$ and $f_2(x) = \lambda^2 x e^{-\lambda x}, \; x > 0$, respectively, where $\lambda > 0$. For service, a customer chooses $P_1$ or $P_2$ randomly with equal probability. Suppose, the probability that the service time for the customer is more than one minute, is $2e^{-2}$. Then the value of $\lambda$ equals __________ (answer in integer).