Probability of a pen cap to rebound around its head when thrown towards a wall

Question

For the sake of simplicity lets assume that the cap is cylinder whose mass, say $M$, is uniformly distributed. Lets it length be $l$ and radius be $R$. The wall is $d$ distance from the initial point. Say i throw it at an angle theta, with its head pointing towards the wall. Obviously $g$ is acting downwards. What is the probability that whole of it's head hits the wall? Also the probability that the head of the cap hits it at an angle. (Assume more parameters if needed)