A storage warehouse in a relatively remote part of a county is protected by a homemade burglary detection system. Once actuated by an intruder, the system sounds a horn and flashes a light for 15 minutes, then saves battery power by shutting down and resetting itself until the next intrusion is detected. Police in three patrol cars have this part of the county as one of their responsibilities, and they routinely drive by the warehouse facility during the hours from dark to dawn.
On average, a patrol car passes the warehouse every 20 minutes, and the time between patrol car arrivals is exponentially distributed. It's the middle of the night and a burglar has just broken into the storage warehouse and set off the alarm. What is the probability that the alarm will shut off before the next police patrol car drives by?