A family consisting of four persons—A, B, C, and D—belongs to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned.
(a) What is the probability that all four family members are assigned to the same station?

Question

A family consisting of four persons—A, B, C, and D—belongs to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned.
(a) What is the probability that all four family members are assigned to the same station?

directrix · Answer

Take a look at #20 here. Then, scroll to the end of the .pdf for additional information. There is no indication who wrote the information about this problem. http://www.math.unt.edu/~johnq/courses/2012fall/3680/sample.pdf