Bayesian+Network

Wiki tutorial:
You have a new burglary alarm at home that is quite reliable at detecting burglars but may also respond at times to earthquake. You also have 2 neighbors, JOHN and MARY, who promise you to call you at work when they hear the alarm. John always calls when he hears the alarm but sometimes confuses the telephone ringing with the alarm and call then. Also, Mary likes loud music and sometimes missed the alarm.

Question: In the burglary system, who is more reliable when burglary happened? Mary or John? Proof by using Bayesian Network.




 * Conditional probability table:



Calculation for P(M|B):

**


 * Calculation for P(B):**




 * Conclusion:**

Since P(J|B) = 0.849017 and P(M|B) = 0.67, so we conclude that John is more reliable than Mary in this burglary system.