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:

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 departmenttwice.

FROM TO PROBABLITY X-ray department Operating rocm Observation room Outprocessing clerk Operating room Cast-itting rocm Observation rocm 45 .15 10 30 . 10 .25 35 30 .25 .70 05 Initial exam at emergency rocm entrance X-ray department Outprocessing clerk Cast-fiting room Observation room Operatng room Cast-fiting room Observation room X-ray department utprocessing clerk Operating rocm X-ray department Outprocessing clerk .05 40 .15 .15 70 Cbservation room