Confidence Intervals · Superchallenge problem

Two independent observations $x_1, x_2$ are taken from a normal population with unknown mean $\mu$ and unknown standard deviation. Someone builds the interval $\bar x \pm \sqrt3\,\dfrac{s}{\sqrt2}$, where $s$ is the sample standard deviation (so they are using a $t$ interval with critical value $\sqrt3$ and 1 degree of freedom). What is the EXACT probability that this interval contains $\mu$?