The classical theorem of Wendel provides an exact formula for the probability that the convex hull of independent symmetrically distributed vectors in ${\mathbb R}^d$ contains the origin as long as the distributions of the vectors are continuous. In this note, we provide an extension to Wendel's theorem for independent random vectors $X_1,\dots,X_n$ with i.i.d components having a (possibly discrete) symmetric distribution of unit variance. As a related observation, we give sharp estimates on the probability that a random linear program of the form ``$\max\langle x,{\mathfrak c}\rangle\quad\mbox{subject to }\langle X_i,x\rangle\leq 1,\;i\leq n$'', is bounded.