Problem For The Day! - 11 - Oct - 2014

Let $X_1,X_2$ and $X_3$ be three i.i.d. exponential distributed random variables with parameter $\lambda = 1$. Let $Y_1 = X_1 + X_2$, $Y_2 = X_1+X_3$ and $Y_3 = X_2 + X_3$. The probability that $\left\{ Y_1 > Y_2>Y_3\right\}$ is

(A) $\frac{1}{2} \quad$ (B) $\frac{1}{3}\quad$ (C) $\frac{1}{6}\quad$ (D) $\frac{5}{6}$