Problem -

Central Hospital in York, Pennsylvania, has an emergency room that is divided into six departments: (1) an initial exam station to treat minor problems or to make a diagnosis; (2) an X-ray department; (3) an operating room; (4) a cast-fitting room; (5) an observation room (for recovery and general observation before final diagnosis or release); and (6) an out processing department (where clerks check out patients and arrange for payment or insurance forms). The probabilities that a patient will go from one department to another are presented in the following table:

a) Simulate the trail followed by 10 emergency room patients. Proceed, one patient at a time, from each one's entry at the initial exam station until he or she leaves throughout-processing. You should be aware that a patient can enter the same department more than once.

b) Using your simulation data, determine the chances that a patient enters the X-ray department twice.