A friend of yours approaches you with the business idea of a private home security service. This private home security service guarantees to either dispatch one of their own five guards immediately if one of their customers sends in an alarm or, in the case that all five guards are responding to other calls, direct the alarm to the local police. The company receives 12 calls per hour, evenly distributed over the course of the day. The local police charges the home security company $500 for every call that the police responds to. It takes a guard, on average, 90 minutes to respond to an alarm.
a. What fraction of the time are incoming alarms directed to the police?
b. How much does the home security company have to pay the local police every month?