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A family consisting of four persons—A, B, C, and D—belongs to a medical clinic that always...

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Statistics

A family consisting of four persons—A, B, C, and D—belongs to amedical clinic that always has a doctor at each of stations 1, 2,and 3. During a certain week, each member of the family visits theclinic once and is assigned at random to a station. The experimentconsists of recording the station number for each member. Supposethat any incoming individual is equally likely to be assigned toany of the three stations irrespective of where other individualshave been assigned.

(a) What is the probability that all four family members areassigned to the same station?


(b) What is the probability that at most three family members areassigned to the same station?


(c) What is the probability that one station has two family membersat it and the others have only one?

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