Problem A.1 Application of Bayes's theorem (20 Marks) A burglar alarm is installed to protect a property. When the alarm is on, if a human is present, they are detected with probability 97%. There is a also a 10% probability of false alarm caused by animals, moving leaves etc. Reading the last-year statistics, it is believed that there is (on average for a given night) a 1% probability of robbery in the neighbourhood. The alarm is switched on every night. If on a certain night the alarm rings what is the probability that a potential burglar is actually on the premises of this property? (5 marks) Explain and justify your answers in a way you find appropriate. (5 marks) How does it compare with the false positive puzzle? (5 marks) . Now we want that if that alarm rings, the probability that there is potential burglar on the premises is at least 80%. What should we require ? (5 marks) Problem A.1 Application of Bayes's theorem (20 Marks) A burglar alarm is installed to protect a property. When the alarm is on, if a human is present, they are detected with probability 97%. There is a also a 10% probability of false alarm caused by animals, moving leaves etc. Reading the last-year statistics, it is believed that there is (on average for a given night) a 1% probability of robbery in the neighbourhood. The alarm is switched on every night. If on a certain night the alarm rings what is the probability that a potential burglar is actually on the premises of this property? (5 marks) Explain and justify your answers in a way you find appropriate. (5 marks) How does it compare with the false positive puzzle? (5 marks) . Now we want that if that alarm rings, the probability that there is potential burglar on the premises is at least 80%. What should we require