2. A burglar alarm is installed in a property shared by John & Mary. It reliably detects burglary, but also is sensitive to weak earthquake events. The tenants promise to call the police when they hear the alarm. John always calls the police when he hears the alarm, but sometimes confuses the alarm with telephone ring. However, he will still call the police even if he is not sure. Mary likes loud music, sometimes misses the alarm. Prior probabilities for the events are as follows

a. Develop a Bayesian Network, incorporate prior probabilities and estimate probability of Alarm Sounding being True

b. What is the probability of burglary occurring given

I. John made the call to Police

II. Mary made the call to Police

III. Both made calls to Police