The Toronto General Hospital 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 outprocessing department (where clerks check out patients). 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 through outprocessing. 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.

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Probability From To Initial exam at 0.45 Х-гау department emergency room entrance Operating room 0.15 0.10 Observation room 0.30 Outprocessing clerk X-ray department Operating room 0.10 0.25 Cast-fitting room Observation room 0.35 Outprocessing clerk 0.30 Operating room Cast-fitting room 0.25 Observation room 0.70 Outprocessing clerk 0.05 Observation room 0.55 Cast-fitting room Х-гаy department 0.05 Outprocessing clerk Operating room 0.40 Observation room 0.15 0.15 Х-гаy department Outprocessing clerk 0.70