Bayesian network calculation

Question

I have a bayesian network like this:

The associated probabilities are:

Now I want to calculate Pr(Fire =T|Tampering = F, Alarm = T). Using Netica, the value is 1. But how can I manually calculate it?

Answer 1

The probability that Alarm=True given Tampering=False and Fire=False is found from your table by looking at the cells where the conditions are met; these are the two lower-left cells with probability 0.99 and 0 respectively. Given that one of these outcomes must occur, it is clear that it has to be the one with Fire=True, so the probability of this outcome is 1, given the conditions.

If we were to calculate the probabilities, we would say that pr(Tampering=F, Fire=T | Tampering=F, Alarm=T) = 0.99 / (0.99 + 0) = 1 and pr(Tampering=F, Fire=T | Tampering=F, Alarm=T) = 0 / (0.99 + 0) = 0.