Solution
= Solution
Let $D=R-L$ be right-arm length minus left-arm length. A <linear combination of jointly normal random variables> is normal, and
$$
\mathbb E D=102-100=2,
$$
while
$$
\operatorname{Var}(D)=2^2+1^2-2\left(\frac12\right)(2)(1)=3.
$$
Thus $D\sim N(2,3)$, and <standardization of a normal random variable> gives
$$
\boxed{\mathbb P(R>L)=\mathbb P(D>0)=\Phi\left(\frac2{\sqrt3}\right)}.
$$