设 $Y_1, Y_2, Y_3$ 是来自总体 $Y \sim\left(\begin{array}{cc}0 & 1 \\ 1-p & p\end{array}\right)(0 < p < 1)$ 的简单随机样本, 令
$$
X_k=\left\{\begin{array}{ll}
1, & Y_1+Y_2+Y_3=k \\
0, & Y_1+Y_2+Y_3 \neq k
\end{array}(k=1,2),\right.
$$
则 $\mathrm{P}\left\{X_1+X_2=1\right\}= $.
$\text{A.}$ $3 p^2+3(1-p)^2$
$\text{B.}$ $3 p(1-p)$
$\text{C.}$ $6 p(1-p)^2$
$\text{D.}$ $6 p^2(1-p)$