A police car is on patrol in a neighborhood known for its ga

A police car is on patrol in a neighborhood known for its gang activities. During a patrol, there is a 65% chance of responding in time to the location where help is needed, else regular patrol will continue. Upon receiving a call, there is a 15% chance for cancellation (in which case normal patrol is resumed) and a 35% chance that the car is already responding to a previous call. When the police car arrives at the scene, there is a 10% chance that the instigators will have fled (in which case the car returns back to patrol) and a 45% chance that apprehension is made immediately. Else officers will search the area. If apprehension occurs, there is a 55% chance of transporting the suspects to the police station, else they are released and the car returns to patrol. Express the probabilistic activities of the police patrol in the form of transition matrix.

Solution