Questions:
- P (JohnCalls|Burglary) ?
- Why?
Source of the image: Artificial Intelligence: A Modern Approach - Third Edition, by Stuart Russell and Peter Norvig.
What do you know about Bayesian networks? I know they exist, but don't understand enough of how it works (i.e., I understand almost nothing). This example would help me gain comprehension about the inter-relation of the variables.
I know that P (JohnCalls|Burglary) would result in the probability of JohnCalls being divided by the probability of Burglary if these were the only two variables and there was a contingency table for just these two. But there is the Alarm in the middle impacting JohnCalls and I don't know what to do with Alarm.
My attempt at solving: using Bayes' Theorem
P(JohnCalls|Burglary) = P(J|B) = ( P(B|J) * P(J) / P(B) )
- P(B): 0.001
- P(J): it depends on the Alarm ringing or not ringing, so I cannot be sure about which probability to take in consideration.
- P(B|J): ??????
