I have been watching a series of lectures on Bayesian Networks and I am getting stuck on a example problem given in most presentations. In the Stanford lecture here
the example given at 21:00. In the alarm bayes net I am confused about how the conditional probability table P(A|B,E) is being filled out. Some of the entires make sense to me but others do not. For example the second to last entry (b=1,e=1,a=0, p(a|b,e)=0) in the table does not seem possible if you have a perfect alarm system. If there is both an earthquake e=1 and burglary b=1 the alarm should always trigger. Furthermore isn't the behavior of the alarm solely dependent on the variables b and e? Why is there an 'a' variable at all? It seems the might be some math baked into this example with bayes rule but I just don't see it.