This would be a better experiment because (1) it is simpler and faster, (2) the feedback is unambiguous, (3) the ability to add is verifiable.
Essentially you supply it with all sums of all pairs of numbers from 0 to 99 and then see if it can compute 100+100.
Thus, a bayesian classifier has to know the classes and the inputs before. It cannot extrapolate from the sets it was trained on, since the bayesian approach does not see numbers as something that some operations are defined on, but only as symbols.
A simple backprop neural network can learn addition, though.
David MacKay wrote a good intro book on Bayesian, neural networks, and related topics: http://www.inference.phy.cam.ac.uk/mackay/itila/
http://www.inference.phy.cam.ac.uk/mackay/itila/Potter.html
Should you buy the MacKay text or one by J.K. Rowling?
By the way, for the addition example , the neural network needs only one example, e.g. 1+1=2, applied repeatedly to discover the addition of any two inputs. There is no extrapolation between examples needed in this case.
See, a bayesian cannot really understand that there are relations between two numbers (like "is bigger than" or "is the following number of"), but a neural network can, since addition is part of a NN.
My personal recommendation on machine learning is 'Pattern Recognition and Machine Learning' by Chris Bishop. But you definately do need a solid mathematical background for that.