Tail of the minimum of exponentials beyond mean plus sd

Let $X_1,X_2,X_3$ be independent random variables with the common probability density function

$$f(x)=\begin{cases}2e^{-2x}, & x>0,\ 0, & \text{otherwise.}\end{cases}$$

Let $Y=\min\{X_1,X_2,X_3\}$, $E(Y)=\mu_y$ and $\mathrm{Var}(Y)=\sigma_y^2$. Then $P(Y>\mu_y+\sigma_y)$ equals __________________