Given $4$ distinct randomly chosen points $x_1$, $x_2$, $x_3$, and $x_4$ in the plane such that the polygonal path from $x_1$ to $x_2$ to $x_3$ to $x_4$ to $x_1$ describes a non-self-intersecting quadrilateral, what is the probability that the quadrilateral is convex?
This question is prompted by the observation that, although arrowheads, darts and chevrons are not rare, the corresponding quadrilateral is seldom mentioned/encountered in the study of elementary geometry.