To make meaningful statements about P and NP problems, you probably need to be able to model your problem as a computational one.
If for example, you model it as a graph, with a peg represented by a node, and a bounce direction to another peg with a directed edge. Assign probabilities to all the edges. Then you cqn simply flood search outwards to the end of the graph, accumulating probabilities by multiplication. Any node on the boundary with probability higher than zero can be reached, given enough balls. This job is clearly in P.
I'm not sure it makes sense to talk about "P" for physical problems without a computational model, but I'm not a complexity theorist
If for example, you model it as a graph, with a peg represented by a node, and a bounce direction to another peg with a directed edge. Assign probabilities to all the edges. Then you cqn simply flood search outwards to the end of the graph, accumulating probabilities by multiplication. Any node on the boundary with probability higher than zero can be reached, given enough balls. This job is clearly in P.
I'm not sure it makes sense to talk about "P" for physical problems without a computational model, but I'm not a complexity theorist