Survival probability of a series system of exponential and gamma lifetimes

Let $X$ and $Y$ denote the lifetimes (in years) of two independent components connected in a series with respective probability density functions

$$f_X(x)=\tfrac12e^{-x/2}, x>0,\quad\text{and}\quad f_Y(y)=\tfrac y4e^{-y/2}, y>0.$$

Then the probability that the system will survive for at least $2$ years, is