Careful consideration is required when combining discrete probability distributions. This is a problem frequently faced in reserves evaluations and has recieved much attention. For example;
But Remaining Proved Reserves are much higher:don't you know how to add up?
Dr Richard Pike, Chief Executive, Royal Society of Chemistry
London SPE Presentation 24 February 2009
Methods for Probabilistic Aggregation of Oil and Gas Field Reserves
SPE Paper 166394
its easy to get it wrong and if you do your results could be misleading.