Similar to the hospital schedule in Example 2-11, supposethat an oper ating room needs to schedule three knee, four hip,and fi ve shoulder surgeries. Assume that all schedules are equallylikely....

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(a) P(all hip surgeries are completed first given that all knee surgeries are last)
A = schedules with all hip surgeries completed first
B = schedules with all knee surgeries last
Total number of schedules =



Number of schedules with all knee surgeries last =



Number of schedules with all hip surgeries first and all knee surgeries last = 1
P(B) =



, P(A ∩ B) =


Therefore, P(A | B) = P(A ∩ B)/P(B) = 1/


=1/126
Alternatively, one can reason that when all knee surgeries are last, there are


remaining schedules and one of these
has all knee surgeries first. Therefore, the solution is 1/

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